QMB 3600-The two liquid products that Knox-Shays Chemical makes

QMB 3600-The two liquid products that Knox-Shays Chemical makes

Subject: Mathematics    / Statistics
Question

1. The two liquid products that Knox-Shays Chemical makes, KS-01 and KS-02, yield excessive amounts of three different pollutants: P1, P2, and P3. The state government has ordered the company to install and to employ antipollution devices. The following table provides the current daily emissions of each of the three pollutants, in kg/1000 liters of product (kilograms per 1000 liters), and the maximum of each pollutant allowed in kg.
Product
Pollutant KS-01 KS-02 MAXIMUM ALLOWED
P1 20 35 40
P2 10 15 20
P3 80 60 50
The manager of the Production Department has approved the installation of two antipollution devices. The emissions from each product can be handled by either device in any proportion. (The emissions are sent through a device only once, that is, the output of one device cannot be the input to the other or back to itself.) The following table shows the percentage of each pollutant from each product that is removed by each device.
Device1 Device2
POLLUTANT KS-01 KS-02 KS-01 KS-02
P1 40 35 30 20
P2 60 60 0 0
P3 50 50 60 85
For example, if the emission from KS-01 is sent through Device 1, 40% of pollutant P1, 60% of pollutant P2, and 50% of pollutant P3 are removed. Manufacturing considerations dictate that KS-01 and KS-02 be produced in the ratio of 1 to 2.

Formulate a single LP model to determine a plan that maximizes the total daily production (amount of KS-01 plus amount of KS-02) while meeting the governmental requirement

2. ABC company is designing a new snack made from air-popped popcorn and natural peanut butter. The objective is to minimize the total cost of these ingredients used, but the final product must contain at least 4 grams of protein, not more than 10 grams of carbohydrate and 2 grams of saturated fat.

a. Identify and define the decision variables.

b. Identify and assign a symbolic name to each additional data value you would have to obtain to be able to formulate an LP model.

c.Formulate a mathematical model using the variable names from part (a) and the symbolic names for the data from part (b).