03 May 1) Selecting the right product mix: a factory has 3 machines (
1) Selecting the right product mix: a factory has 3 machines (M1, M2 and M3) and it manufactures two products (P and Q). The demand for both the products is far greater than the capacity of the factory: ? Market price for P is $30 per unit, and $40 per unit for Q ? Raw Material cost of P is $5 per unit, and $10 per unit for Q ? Making one unit of P takes 20 minutes on M1, 20 minutes on M2 and 30 minutes on M3. Making one unit of Q takes 15 minutes on M1, 15 minutes on M2 and 30 minutes on M3. ? The factory works 8 hours a day, 5 days a week. ? It costs $100 per day to run the factory (including wages, rent, utilities etc). ? Assume a steady state operation and keep in mind that this is a business so maximum profitability is the goal. BRIEFLY SHOW OR EXPLAIN YOUR THOUGHT PROCESS WHEN ANSWERING THE QUESTIONS BELOW: 1. To maximize its profits, the company should sell a) Only product P b) Only product Q c) A mixture of P and Q . 2. The maximum profit that the company can make in one day is a) $ 320 b) $ 480 c) $ 380 3. The factory makes a process improvement and reduces the total time taken to make product Q. The total labor input for product Q was previously 60 minutes per unit, and with the new process it only takes 50 minutes per unit – 5 minutes on M1, 5 minutes on M2 and 40 minutes on M3. The maximum profit the company can now make in one day with either P or Q is a) $ 260 b) $ 300 c) $ 500 4. The company decides to discontinue the “process improvement”. They discover that they can decrease the time it takes to make Q on M3 from 30 min to 20 min. At the same time the demand for Q is no more than 18 units a day. What is the profit for the company in one day now a) $ 540 b) $ 640 c) $ 440 5. In addition to the assumptions in 4, the company adds a third product to the mix. The company’s marketing department has to decide which products to push. Material cost of product R is $10 per unit and price is $20. Product R should be pushed in the market if the time it uses on M3 is less than: a) 10 min b) 6.66 mi
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