BUS 365. Management Science Homework
BUS 365. Management Science Homework
The country of Milkandhoney produces only three commodities: machinery, steel, and auto- mobiles. All other goods—food, clothing, energy—are imported. The Minister of
the Economy is responsible for economic planning, and she knows the welfare of the country is best served by maximizing the net dollar value of exports (that is, the
value of the exports from which is deducted the cost of the materials imported to produce those exports). The country of Milkandhoney can sell all the steel, automobiles, or machinery it can produce on the world market at prices of $800 per unit for steel, $ 21,000 per
unit for automobiles, and $ 39,000 per unit for machinery. In order to produce 1 unit of steel, it takes 0.005 units of machinery, 0.002 units of automobiles, 1 unit of ore purchased on the world market for $ 150 per unit, and
other imported materials costing $ 50. In addition, it takes one one-hundredth worker-year of labor to produce each unit of steel. Milkandhoney’s steel mills have a
rated capacity of 6.7 million units per year. To produce 1 unit of automobiles, it takes 0.75 unit of steel, 0.02 units of machinery, and 0.4 worker-year of labor. In addition, it takes $ 10,400 worth of imported
materials to produce each unit of automobiles. Automobile capacity is 3.1 million units per year. To produce 1 unit of machinery requires 0.03 units of automobiles, 1.1 unit of steel, and 1.25 worker-years of labor, in addition to $ 17,000 for items imported from
outside the country. The capacity of the machinery plants is 2.8 million units per year. The total personnel available for labor in Milkandhoney is 5.5 million persons per year. Formulate a linear-programming model to determine the production mix that will maximize net dollar value of exports. NOTE: Be extremely careful in defining your variables.
Assignment:You are to write a formal letter to Alvaro Pena Nieto, the Minister of the Economy of the country of Milkandhoney; he needs to know the number of automobiles, units of
steel, and units of machinery the country should manufacture, the number of man-years of labor it will need to hire, as well as the number of each (auto, machinery,
steel) that it will export. Finally, your memo should indicate the earned export revenue that the country should anticipate, as well as the unemployment level that the
country will face. Of particular interest to Mr. Pen ̃a Nieto is whether he should support the construction of a new steel mill that would add 100,000 tons to the country’s steel-making
capacity, or the construction of a plant that would allow as many as 100,000 pieces of industrial machinery to be produced. Because of the availability of engineers in
the country, only one of these two proposals can be undertaken. Your memo should offer a recommendation to Mr. Pen ̃a Nieto. He must also determine whether he should support a proposal being considered by Congress to grant as many as 200,000 work visas to the citizens of the neighboring
country of Lower Slobovia who would then immigrate to Milkandhoney and work in its factories. What would the impact of such legislation have on the economy of
Milkandhoney? This letter must be written in correct and proper English, and be quite formal; you are a consultant writing to the to Minister of the Economy of a country. Make sure
the tone is proper for someone of his stature.Your letter should be printed on a letterhead,It should be accompanied by a printout of the output of the Excel spreadsheet.
The Excel file is a little different. Only need seven constraints in Column A need to be filled out. Only need three variable types, for example if I am correct I
think it would be steel, automobiles and machinery. You only need to use two on the right and one on the left for the columns. The teacher said they didn’t want to
create another excel file so Column C-J doesn’t need anything it in. They said the numbers can still be generated correctly.
S=SteelA=AutomobilesM=Machinery
S 1= Number of units of steel produced A 1= Number of units of automobiles producedM 1= Number of units of machinery produced
Maximize the net dollar value of exports
S= Number of units of steel produced- Some are going to be exported and some are going to be used to make automobiles and machinery.
Max 800 (Units of steel exported)
Units of steel exported= Units of steel produced-units of steel used to make automobiles and machinery.
Units of steel exported= S-0.75 A-1.1 M
800 (S – 0.75 A – 1.1 M) + 21,000 (A – 0.002 S – 0.03 M) + 39,000 (M -0.005 S – 0.02 A) – 200 S – 10,400 A – 17,000 M
Units of automobiles exported = Units of automobiles produced – Units of automobiles used to make steel and machinery.
For Steel: 800 – 42 – 195 – 200 = 363
For Automobiles: 21,000 – 600 – 780 – 10,400 = 9,220
For Machinery: 39,000 – 880 – 630 – 17,000 = 20,490
Max= 363 S + 9,220 A + 20,490 M
S.T. (Subject Two)
S ≤ 6,700,000
A ≤ 3,100,000
M ≤ 2,800,000
0.01 S + 0.4 A + 1.25 M ≤ 5,500,000
Amount of steel produced ≥ Amount of steel needed to make automobiles and machinery.
S ≥ 0.75 A + 1.1 M
A ≥ 0.002 S + 0.03 M
M ≥ 0.05 + 0.02 A
S 2= Number of units of steel exported
A 2= Number of units of Automobiles exported
M 2= Number of units of Machinery exported
Max= 800 S 2 + 21,000 A 2 + 39,000 M 2 – 200 S 1 – 10,400 A 1 – 17,000 M 1
S.T. (Subject Two)
S 2 = S 1 – 0.75 A 1 – 1.1 M 1
A 2 = A 1 – 0.002 S 1 – 0.03 M 1
M 2= M 1 – 0.005 S 1 – 0.02 A 1
September 3, 2017
The Honorable Gordon Smith Ministry of the Economy of Milkandhoney1 Honey LaneCapital City, MAH 10001
Dear Mr. Smith:
Thank you very much for giving me the opportunity to work on determining the industrial output that will maximize export revenues for Milkandhoney.
Milkandhoney’s industrial output is restricted to three different commodities; steel, automobiles and machinery, the production of which is entirely controlled by the
government. The steel mills of the country have a total annual capacity of 9,100,000 tons, the automobile plants can manufacture 2,700,000 vehicles and the remaining
industrial factories can produce 1,800,000 machines. The labor force in the country comprises 6,000,000 individuals and a secondary goal of the country is to ensure
full employment.
In order to determine the optimum industrial output for the country, my firm created a model of the economy that took into consideration the goals of the country’s
government and the constraints under which these policies were to be implemented. Using Linear Programming, a powerful computer simulation tool, our firm arrived at
the following recommendations:
– Produce a total of 6,420,000 tons of steel, none of which should be exported. 42 percent of the steel produced should be used to manufacture automobiles, and
58 percent should be used to make machinery.
– Produce a total of 2,450,000 automobiles, 40 percent of which should be exported, 12 percent of which should be used to make steel, and 38 percent of which
should be used to make machinery.
– Produce a total of 1,565,000 pieces of machinery, 65 percent of which would be exported, 10 percent of which should be used to make steel, and 25 percent of
which should be used to make automobiles.
The unemployment rate in Milkandhoney would be 4.7 percent, with 5,718,000 people employed and 282,000 unemployed, which would be considered a normal frictional
unemployment level. Given this unemployment level, it is not advised to offer guest-worker visas to citizens of Lower Slobovia.
The total export revenue for Milkandhoney would be $ 3.17 trillion, and imports would represent $ 1.1 trillion, for a total net export revenue of $ 2.07 trillion.
Please do not hesitate to contact me if you have any questions regarding these recommendations.
Sincerely,
Firstname LastnameJunior Consultant