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In: Operations Management

Integer Programming Problem (Chapter 6) A manufacturer can sell product 1 at a price of $30...

Integer Programming Problem (Chapter 6)

A manufacturer can sell product 1 at a price of $30 per unit and product 2 at a price of $40 per unit. Three units of raw material and 1.5 labor hours are needed to manufacturer one unit of product 1. Six units of raw material and 2 labor hours are need to manufacture one unit of product 2. The unit variable cost for product 1 is $20, and for product 2 is $20. A total of 15,000 units of raw material and 8,000 labor hours are available. If any product 1 is produced, a setup cost of $15,000 is incurred; if any product 2 is produced, a setup cost of $35,000 is incurred. Determine how to maximize the manufacturer’s profit.

a. What is the effective capacity for product 1 and product 2, respectively?

b. In the optimal solution, which product(s) will be manufactured? What is the optimal production quantity? What is the optimal profit?

Please use excel to solve the problem and show formulas.

Expert Solution

We will setup Excel with integer programming as shown in below excel screenshots to solve this problem.

We will setup Solver with Decision variables, objective function and constraints.

Click on Solve to get optimal solution

a.

Effective or maximum capacities for Product 1 will be when the other Product (Product 2) production is zero and similarly for the other product.

Product 1 -> With total capacity of 15000 raw material, maximum units of product 1 which can be produced is 15000/3 = 5000. Also with total capacity of 8000 labor hours, maximum units of product1 which can be produced is 8000/ 1.5= 5333.33. Since both conditions need to be met, effective capacity of Product 1 is 5000.

Product 2 -> With total capacity of 15000 raw material, maximum units of product 2 which can be produced is 15000/6 = 2500. Also with total capacity of 8000 labor hours, maximum units of product 2 which can be produced is 8000/ 2= 4000. Since both conditions need to be met, effective capacity of Product 2 is 2500.

b. Looking at the output of Solver, we can see that the optimal solution is to only produce Product 1. To producce 5000 units of Product 1 to get the total optimal profit of $35,000.

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keosha answered 6 days ago

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