The Charm City Manufacturing Company would like to maximize the profit of manufacturing three products. The time in hours required for each product in each production department is tabled below, along with the profit for each product. Product 1 Product 2 Product 3 Department A 28 18 30 Department B 8 10 10 Department C 8 6 5 Profit $120 $100 $110 Currently labor assignments provide for 4200 hours in Department A, 2000 hours in Department B, and 2200 hours in Department C. Charm City wants to produce at least 60 units of Product 1. Answer the following questions by using the ranging (sensitivity analysis) results from Question 2. Do NOT solve the problem again by using any computer software.
a. If the profit from a unit of Product 1 increases from $120 to $150, will the optimal number of units of the three products manufactured change? Will the total profit change? If they change, what will be the new optimal solution and the new total profit?
b. The company has an opportunity to get some extra hours in Department A. What is the maximum price the company should pay for each additional hour in Department A, and how many hours should they get at that price?
c. The company has an opportunity to get some extra hours in Department B. What is the maximum price the company should pay for each additional hour in Department B, and how many hours should they get at that price?