Motor Startup You are a small car manufacturer with an assembly line in Detroit

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Motor Startup

You are a small car manufacturer with an assembly line in Detroit and an assembly line in Dallas Your Plant in Detroit has 3 thousand tons of steels available for production until next month. The plant in Detroit is closer to the steel mill, hence you can get them for about $250 per ton. Since it is an older plant, you have more employee at this facility (about 10,000 labor hours are available this month), but they are also paid more ($25 per hour) because they are at the plant for a longer period of time. He energy cost in Detroit is about $5 per kilowatt. You have access to unlimited amount of electricity in Detroit.

Your Dallas plant I newer plant, but it is much further away from the steel mill. You are sourcing the steel for $350 per ton and you have about 2,500 tons of steel available for production until next month. You don’t have as many employees at this facility (about 7,000) labor hours are available this month), but they are paid at $19.50 per hour. The energy cost in Dallas is 40% less than in Detroit. You also have access to unlimited amount of electricity in Dallas.

You are producing two types of vehicles at these two facilities, small truck and sedan. A simplified production requirement for each product are as follows: producing a small truck need 25 labor hours, 3 tons of steels, and 40 kilowatt to manufacture; creating a sedan require 19 labor hours, 2 tons of steels, and 25 kilowatt to manufacture. The requirement is the same for both facilities.

Your major markets are New York City, Charlotte, Orlando, St. Louis, Chicago, Los Angeles, and Seattle. The cost of transportation from each facility is presented below:

Cost per unit shipped to destination:

Detroit Dallas   

City

Small Truck

Sedan

Small Truck

Sedan

New York

$100

$90

Charlotte

$150

$120

$200

$150

Orlando

$100

$70

St. Luis

$70

$50

$50

$40

Chicago

$30

$20

Los Angeles

$150

$140

Seattle

$200

$180

Each small truck may be sold for $5,500 while each sedan may be sold for $2,900.

You expect the demand for sedan is about the same across all the city at 60 per city. However, the demand for small trucks is much lower with New York, Chicago, and Seattle each need about 20 trucks per city. Charlotte and St. Louis needs about 25 trucks for each city. Orlando and Los Angeles need only 30 trucks for each city.

Product Mix Question:

Assuming that you can sell everything that you can produce, what should be the production mix for your Detroit and Dallas (without the transportation cost) to minimize your bottom line. Provide the system of linear equations and solve it using Excel Solver. Print out the sensitivity report and discuss (describe the solution.

Would you like to have more labor or more steel? Explain.

Transportation Question:

Suppose you manufacture 150 small truck and 250 sedan from both Detroit and Dallas plant (small trucks and sedan), how should you satisfy the demand from each city to minimize your total cost? Provide the system of linear equations and solve it using Excel Solver. Print out sensitivity report and discuss (describe) the solution. How many small truck and sedan are shipped from Detroit? How many small truck and sedan are shipped from Dallas?

Combined Product Mix and Transportation Question:

Since we live in the “real” world, what is the optimum profit you can generate from this company for this month? Provide the system of linear equations and solve it using Excel Solver. Print out the sensitivity report and discuss (describe) the solution.

A. Identify the most profitable vehicle-route combination. Identify the least profitable vehicle-route combination.

B. Which city generate the highest profit for you?

C. Which city is most unhappy with your service (the city that has the highest unfulfilled order)?

D. Explain, using the sensitivity report, which resource would you want to have more of, steel or labor (identify which facility you want the resource in).

E. If you can produce more sedan or truck, where would you send?

City

Small Truck

Sedan

Small Truck

Sedan

New York

$100

$90

Charlotte

$150

$120

$200

$150

Orlando

$100

$70

St. Luis

$70

$50

$50

$40

Chicago

$30

$20

Los Angeles

$150

$140

Seattle

$200

$180

Explanation / Answer

Product mix problem without transportation:

Decision variables are the number of trucks and sedans (finished products) to be produced.

Objective function is to mamimize the total c of production.

Constraints are on account of availability of inputs, steel, labour hours etc.

The given information about the availability and price/cost of raw materials as well their requirements are given in the excel sheet as follows:

Revised solution with energy cost as $5 per KWH is as follows:

Outcome remains the same that is to produce 400 small trucks and no sedan. Binding constraint is availability of labour hours. So more production means additional labor hours.

The net result for the product-mix problem is to go for production of small trucks as profit per unit is more as compared to sedan. Secondly the binding constraint is labor hours so far more production more labor hours are required. Quantity of steel is available.

Detroit Decision Variables Small Trucks Sedan Number 400 0 Objective function Co-efficients 4118.6 1921 Objective values $ 1647440 0 1647440 Constraints Required Available Steel Qty. Tons 3 2 1200 3000 Steel-Price/ton 250 250 Steel cost/unit 750 500 Labour Qty. Hours 25 19 10000 10000 Labour Price/hour 25 25 Labor cost/unit 625 475 Enegry Qty KWH 40 25 16000 no limit Energy-Price/KWH 0.16 0.16 Energy cost/unit 6.4 4

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