MAT540 All Quizes Latest 2017 March

Subject: General Questions    / General General Questions
Question
MAT540 Week 2 Quiz 1 Latest 2017 March

Question 1

2 out of 2 points

Probabilistic techniques assume that no uncertainty exists in model parameters.

Question 2

2 out of 2 points

In general, an increase in price increases the break even point if all costs are held constant.

Question 3

2 out of 2 points

If variable costs increase, but price and fixed costs are held constant, the break even point will decrease.

Question 4

2 out of 2 points

Fixed cost is the difference between total cost and total variable cost.

Question 5

0 out of 2 points

The events in an experiment are mutually exclusive if only one can occur at a time.

Question 6

2 out of 2 points

A continuous random variable may assume only integer values within a given interval.

Question 7

2 out of 2 points

P(A | B) is the probability of event A, if we already know that event B has occurred.

Question 8

2 out of 2 points

A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room?

Question 9

2 out of 2 points

EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even?

Question 10

2 out of 2 points

If the price increases but fixed and variable costs do not change, the break even point

Question 11

2 out of 2 points

The indicator that results in total revenues being equal to total cost is called the

Question 12

2 out of 2 points

The expected value of the standard normal distribution is equal to

Question 13

2 out of 2 points

In a binomial distribution, for each of n trials, the event

Question 14

2 out of 2 points

The area under the normal curve represents probability, and the total area under the curve sums to

Question 15

2 out of 2 points

Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000.

Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point.

Question 16

2 out of 2 points

A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point.

Question 17

2 out of 2 points

A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point.

Question 18

2 out of 2 points

The variance of the standard normal distribution is equal to __________.

Question 19

2 out of 2 points

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration?

Question 20

0 out of 2 points

Wei is considering pursuing an MS in Information Systems degree. She has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Wei will be accepted by at least one of the two universities? {Express your answer as a percent. Round (if necessary) to the nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20}

MAT540 Week 3 Quiz 2 Latest 2017 March

Question 1

2 out of 2 points

Probability trees are used only to compute conditional probabilities.

Question 2

2 out of 2 points

If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)

Question 3

2 out of 2 points

Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

Question 4

2 out of 2 points

The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are.

Question 5

0 out of 2 points

Both maximin and minimin criteria are optimistic.

Question 6

0 out of 2 points

The maximin approach involves choosing the alternative with the highest or lowest payoff.

Question 7

2 out of 2 points

Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret.

Question 8

2 out of 2 points

Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.

Question 9

2 out of 2 points

A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A’s. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

Question 10

2 out of 2 points

The chi-square test is a statistical test to see if an observed data fit a _________.

Question 11

2 out of 2 points

Determining the worst payoff for each alternative and choosing the alternative with the best worst is called

Question 12

2 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

If the group chooses to minimize their maximum regret, what activity will they choose?

Question 13

2 out of 2 points

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

Question 14

0 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

What is the conservative decision for this situation?

Question 15

2 out of 2 points

A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Note: Write your answers with two places after the decimal, rounding off as appropriate.

Question 16

2 out of 2 points

A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate.

Question 17

2 out of 2 points

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40, what is the numerical maximum expected value?

Question 18

0 out of 2 points

The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

What is the numerical value of the maximin?

Question 19

0 out of 2 points

Consider the following decision tree.

What is the expected value for the best decision? Round your answer to the nearest whole number.

Question 20

0 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is the EVPI for this situation?

MAT540 Week 7 Quiz 3 Latest 2017 March

Question 1

2 out of 2 points

The following inequality represents a resource constraint for a maximization problem:

X + Y ? 20

Question 2

2 out of 2 points

In minimization LP problems the feasible region is always below the resource constraints.

Question 3

2 out of 2 points

In a linear programming problem, all model parameters are assumed to be known with certainty.

Question 4

2 out of 2 points

If the objective function is parallel to a constraint, the constraint is infeasible.

Question 5

2 out of 2 points

Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

Question 6

2 out of 2 points

Surplus variables are only associated with minimization problems.

Question 7

2 out of 2 points

A feasible solution violates at least one of the constraints.

Question 8

2 out of 2 points

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

Question 9

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

This linear programming problem is a:

Question 10

2 out of 2 points

Which of the following statements is not true?

Question 11

2 out of 2 points

Decision variables

Question 12

2 out of 2 points

The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

Question 13

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

Which of the following constraints has a surplus greater than 0?

Question 14

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

The equation for constraint DH is:

Question 15

2 out of 2 points

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

Question 16

2 out of 2 points

The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

Question 17

2 out of 2 points

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a maximization, which extreme point is the optimal solution?

Question 18

2 out of 2 points

Max Z = $3x + $9y

Subject to: 20x + 32y ? 1600

4x + 2y ? 240

y ? 40

x, y ? 0

At the optimal solution, what is the amount of slack associated with the second constraint?

Question 19

2 out of 2 points

Consider the following minimization problem:

Min z = x1 + 2×2

s.t. x1 + x2 ? 300

2×1 + x2 ? 400

2×1 + 5×2 ? 750

x1, x2 ? 0

Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

Question 20

2 out of 2 points

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation.

MAT540 Week 9 Quiz 4 Latest 2017 March

Question 1

2 out of 2 points

When using a linear programming model to solve the “diet” problem, the objective is generally to maximize profit.

Question 2

2 out of 2 points

Fractional relationships between variables are permitted in the standard form of a linear program.

Question 3

2 out of 2 points

A constraint for a linear programming problem can never have a zero as its right-hand-side value.

Question 4

2 out of 2 points

A systematic approach to model formulation is to first construct the objective function before determining the decision variables.

Question 5

2 out of 2 points

In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.

Question 6

2 out of 2 points

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

Question 7

2 out of 2 points

The following types of constraints are ones that might be found in linear programming formulations:

1.

?

2.

=

3.

>

Question 8

2 out of 2 points

Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility.

What is the demand constraint for plant B?

Question 9

2 out of 2 points

The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit?
MAT540 All Quizes Latest 2017 March
Subject: General Questions    / General General Questions
Question
MAT540 Week 2 Quiz 1 Latest 2017 March

Question 1

2 out of 2 points

Probabilistic techniques assume that no uncertainty exists in model parameters.

Question 2

2 out of 2 points

In general, an increase in price increases the break even point if all costs are held constant.

Question 3

2 out of 2 points

If variable costs increase, but price and fixed costs are held constant, the break even point will decrease.

Question 4

2 out of 2 points

Fixed cost is the difference between total cost and total variable cost.

Question 5

0 out of 2 points

The events in an experiment are mutually exclusive if only one can occur at a time.

Question 6

2 out of 2 points

A continuous random variable may assume only integer values within a given interval.

Question 7

2 out of 2 points

P(A | B) is the probability of event A, if we already know that event B has occurred.

Question 8

2 out of 2 points

A bed and breakfast breaks even every month if they book 30 rooms over the course of a month. Their fixed cost is $4200 per month and the revenue they receive from each booked room is $180. What their variable cost per occupied room?

Question 9

2 out of 2 points

EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even?

Question 10

2 out of 2 points

If the price increases but fixed and variable costs do not change, the break even point

Question 11

2 out of 2 points

The indicator that results in total revenues being equal to total cost is called the

Question 12

2 out of 2 points

The expected value of the standard normal distribution is equal to

Question 13

2 out of 2 points

In a binomial distribution, for each of n trials, the event

Question 14

2 out of 2 points

The area under the normal curve represents probability, and the total area under the curve sums to

Question 15

2 out of 2 points

Administrators at a university are planning to offer a summer seminar. The costs of reserving a room, hiring an instructor, and bringing in the equipment amount to $3000.

Suppose that it costs $25 per student for the administrators to provide the course materials. If we know that 20 people will attend, what price should be charged per person to break even? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point.

Question 16

2 out of 2 points

A production run of toothpaste requires a fixed cost of $100,000. The variable cost per unit is $3.00. If 50,000 units of toothpaste will be sold during the next month, what sale price must be chosen in order to break even at the end of the month? Note: please report the result as a whole number, rounding if necessary and omitting the decimal point.

Question 17

2 out of 2 points

A production process requires a fixed cost of $50,000. The variable cost per unit is $25 and the revenue per unit is projected to be $45. Find the break-even point.

Question 18

2 out of 2 points

The variance of the standard normal distribution is equal to __________.

Question 19

2 out of 2 points

Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category.

If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration?

Question 20

0 out of 2 points

Wei is considering pursuing an MS in Information Systems degree. She has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Wei will be accepted by at least one of the two universities? {Express your answer as a percent. Round (if necessary) to the nearest whole percent and omit the decimal. For instance, 20.1% would be written as 20}

MAT540 Week 3 Quiz 2 Latest 2017 March

Question 1

2 out of 2 points

Probability trees are used only to compute conditional probabilities.

Question 2

2 out of 2 points

If two events are not mutually exclusive, then P(A or B) = P(A) + P(B)

Question 3

2 out of 2 points

Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

Question 4

2 out of 2 points

The equal likelihood criterion assigns a probability of 0.5 to each state of nature, regardless of how many states of nature there are.

Question 5

0 out of 2 points

Both maximin and minimin criteria are optimistic.

Question 6

0 out of 2 points

The maximin approach involves choosing the alternative with the highest or lowest payoff.

Question 7

2 out of 2 points

Using the minimax regret criterion, we first construct a table of regrets. Subsequently, for each possible decision, we look across the states of nature and make a note of the maximum regret possible for that decision. We then pick the decision with the largest maximum regret.

Question 8

2 out of 2 points

Assume that it takes a college student an average of 5 minutes to find a parking spot in the main parking lot. Assume also that this time is normally distributed with a standard deviation of 2 minutes. Find the probability that a randomly selected college student will take between 2 and 6 minutes to find a parking spot in the main parking lot.

Question 9

2 out of 2 points

A professor would like to utilize the normal distribution to assign grades such that 5% of students receive A’s. If the exam average is 62 with a standard deviation of 13, what grade should be the cutoff for an A? (Round your answer.)

Question 10

2 out of 2 points

The chi-square test is a statistical test to see if an observed data fit a _________.

Question 11

2 out of 2 points

Determining the worst payoff for each alternative and choosing the alternative with the best worst is called

Question 12

2 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

If the group chooses to minimize their maximum regret, what activity will they choose?

Question 13

2 out of 2 points

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

Question 14

0 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

Weather

Cold Warm Rainy

S1 S2 S3

Bike: A1 10 8 6

Hike: A2 14 15 2

Fish: A3 7 8 9

What is the conservative decision for this situation?

Question 15

2 out of 2 points

A brand of television has a lifetime that is normally distributed with a mean of 7 years and a standard deviation of 2.5 years. What is the probability that a randomly chosen TV will last more than 8 years? Note: Write your answers with two places after the decimal, rounding off as appropriate.

Question 16

2 out of 2 points

A life insurance company wants to update its actuarial tables. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 71 years and a standard deviation of 3.5 years. What proportion of the plan participants are expected to see their 75th birthday? Note: Write your answers with two places after the decimal, rounding off as appropriate.

Question 17

2 out of 2 points

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.

If the probability of brisk business is .40, what is the numerical maximum expected value?

Question 18

0 out of 2 points

The quality control manager for ENTA Inc. must decide whether to accept (a1), further analyze (a2) or reject (a3) a lot of incoming material. Assume the following payoff table is available. Historical data indicates that there is 30% chance that the lot is poor quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance that the lot is good quality (s3).

What is the numerical value of the maximin?

Question 19

0 out of 2 points

Consider the following decision tree.

What is the expected value for the best decision? Round your answer to the nearest whole number.

Question 20

0 out of 2 points

A group of friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of enjoyment for each activity under the various weather conditions.

If the probabilities of cold weather (S1), warm weather (S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is the EVPI for this situation?

MAT540 Week 7 Quiz 3 Latest 2017 March

Question 1

2 out of 2 points

The following inequality represents a resource constraint for a maximization problem:

X + Y ? 20

Question 2

2 out of 2 points

In minimization LP problems the feasible region is always below the resource constraints.

Question 3

2 out of 2 points

In a linear programming problem, all model parameters are assumed to be known with certainty.

Question 4

2 out of 2 points

If the objective function is parallel to a constraint, the constraint is infeasible.

Question 5

2 out of 2 points

Graphical solutions to linear programming problems have an infinite number of possible objective function lines.

Question 6

2 out of 2 points

Surplus variables are only associated with minimization problems.

Question 7

2 out of 2 points

A feasible solution violates at least one of the constraints.

Question 8

2 out of 2 points

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?

Question 9

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

This linear programming problem is a:

Question 10

2 out of 2 points

Which of the following statements is not true?

Question 11

2 out of 2 points

Decision variables

Question 12

2 out of 2 points

The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?

Question 13

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

Which of the following constraints has a surplus greater than 0?

Question 14

2 out of 2 points

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*.

The equation for constraint DH is:

Question 15

2 out of 2 points

Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

Question 16

2 out of 2 points

The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?

Question 17

2 out of 2 points

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a maximization, which extreme point is the optimal solution?

Question 18

2 out of 2 points

Max Z = $3x + $9y

Subject to: 20x + 32y ? 1600

4x + 2y ? 240

y ? 40

x, y ? 0

At the optimal solution, what is the amount of slack associated with the second constraint?

Question 19

2 out of 2 points

Consider the following minimization problem:

Min z = x1 + 2×2

s.t. x1 + x2 ? 300

2×1 + x2 ? 400

2×1 + 5×2 ? 750

x1, x2 ? 0

Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25

Question 20

2 out of 2 points

A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.

What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation.

MAT540 Week 9 Quiz 4 Latest 2017 March

Question 1

2 out of 2 points

When using a linear programming model to solve the “diet” problem, the objective is generally to maximize profit.

Question 2

2 out of 2 points

Fractional relationships between variables are permitted in the standard form of a linear program.

Question 3

2 out of 2 points

A constraint for a linear programming problem can never have a zero as its right-hand-side value.

Question 4

2 out of 2 points

A systematic approach to model formulation is to first construct the objective function before determining the decision variables.

Question 5

2 out of 2 points

In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.

Question 6

2 out of 2 points

In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.

Question 7

2 out of 2 points

The following types of constraints are ones that might be found in linear programming formulations:

1.

?

2.

=

3.

>

Question 8

2 out of 2 points

Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the 3 different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility.

What is the demand constraint for plant B?

Question 9

2 out of 2 points

The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the optimal daily profit?

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