## Satisfying demand of clutch systems

Provide a printout of the formulation of each problem in a word document and provide a printout

of the Excel solution where asked to solve using Excel Solver.

1. Eaton Corp. has to satisfy demand of clutch systems to 3 General Motors plants. They have

two warehouses where they stock the product. The demand at plant 1 is 600 units. The

demand at plant 2 is 800 units, and the demand at plant 3 is 400 units. Warehouse 1 has an

inventory of 800 units and Warehouse 2 has an inventory of 1000 units. Given the shipping

costs/unit below, they need to determine how product should be shipped between the

warehouses and the plants.

From To Plant

Warehouse $1 $2 $3

1 $4 $4 $2

2 $3 $5 $5

Transportation Costs ($)

a. Solve this problem with a heuristic. Explain your heuristic and provide the heuristic

solution.

b. Write a formulation for this problem. Write it out with equations as well as in tableau

format.

c. Solve this problem with the Excel Solver. What is the difference in cost between the

heuristic solution and the optimal solution?

2. A company faces the following demands during the next 4 months, with the following

production costs. They incur inventory costs of $3/month/unit. At the beginning of January

they have 500 units on-hand.

Jan Feb Mar Apr

Demand 1000 3000 2500 3500

Prod. $ 40 25 35 30

They wish to determine the optimal production schedule that will minimize production and

inventory costs.

a. Write a formulation for this problem. Write it out in equations.

b. Try using logic to determine what the optimal answer will be.

3. Highland’s TV-Radio Store must determine how many TVs and radios to keep in stock (the

store stocks only TVs and radios). A TV requires 10 sq. ft. of floor space, whereas a radio

requires 4 sq. ft; 200 sq. ft. of floor space is available. A TV will earn Highland $60 in

profits, and a radio will earn $20. Marketing requirements dictate that at least 60% of all

appliances in stock be radios. Finally, a TV ties up $200 in capital, and a radio $50.

Highland wants to have at most $3000 worth of capital tied up at any time.

a. Formulate an IP that can be used to maximize Highland’s profit. Solve it using Excel.

b. How much more profit could be attained if Highland rented another 50 sq. ft. of floor

space? How much should Highland be willing to pay for this extra footage?

c. How much more profit could be attained if marketing changed their requirement so that

only 40% of all appliances in stock be radios (keeping the floor space at 200 sq. ft.)?

d. How much more profit could be attained if Highland was willing to have $3500 worth of

capital tied-up (keeping the floor space at 200 sq. ft. and the marketing requirement at

40%)? How should Highland decide if it is worthwhile to increase this value?

4. You are in charge of loading cargo ships at a major East Coast port. You have been asked to

prepare a loading plan for a freighter bound for Africa. An agricultural commodities dealer

would like to transport the following products aboard this ship:

Commodity Tons Avail. Volume/ton

(cubic ft)

Profit/ton

($)

1 4000 40 70

2 3000 25 50

3 2000 60 60

4 1000 50 80

You can elect to load any and/or all of the available product. However, the ship has 3 cargo

holds with the following capacity restrictions:

Cargo Hold Weight Capacity

(tons)

Vol. Capacity

(cubic ft)

Forward 3000 100,000

Center 5000 150,000

Rear 2000 120,000

More than one type of commodity can be placed in the same cargo hold. However, the ship

must be balanced, so the weight in the forward hold must be within 10% of the weight in the

rear hold, and the center hold must be assigned between 40 and 60% of the total weight.

Write a linear program that will maximize profits. You don’t need to solve it.

Hint: Define your variables as: Xij = tons of commodity i loaded into cargo hold j