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operations research

1. Two machines are used to produce two types of products. A unit of Product 1 requires 1 hour of processing time on Machine 1, and 4 hours of processing time on Machine 2. A unit of Product 2 requires 1 hour of processing time on Machine 1 , and 1 hour of processing time on Machine 2 . Weekly processing time available on each machine is 40 hours and 100 hours respectively. Selling one unit of Product 1 will generate $600 net profit. Selling one unit of Product 2 will generate $300 net profit. a) Model the problem to maximize the profit and solve it. b) Find the shadow prices for Machine 1 and Machine 2. c) If you can increase the capacity of the both machines, which machine should you give priority? Why? d) Should you increase the availability of Machine 1 at at additional cost of $150 per hour? Why? e) Should you increase the availability of Machine 2 at an additional cost of $150 per hour? Why? f) Suppose that the unit profit for the Product 1 and Product 2 are changed to $405 and $135, respectively. Will the current optimal solution remain the same? g) Suppose that the unit profit for the Product 1 is fixed at $500. What is the range of unit profit for Product 2 that will keep the optimal solution unchanged? Two machines are used to produce two types of products. A unit of Product 1 requires 1 hour of processing time on Machine 1, and 4 hours of processing time on Machine 2. A unit of Product 2 requires 1 hour of processing time on Machine 1, and 1 hour of processing time on Machine 2 . Weekly processing time available on each machine is 40 hours and 100 hours respectively. Selling one unit of Product 1 will generate $600 net profit. Selling one unit of Product 2 will generate $300 net profit. a) Model the problem to maximize the profit and solve it. b) Find the shadow prices for Machine 1 and Machine 2. c) If you can increase the capacity of the both machines, which machine should you give priority? Why? d) Should you increase the availability of Machine 1 at an additional cost of $150 per hour? Why? e) Should you increase the availability of Machine 2 at an additional cost of $150 per hour? Why? f) Suppose that the unit profit for the Product 1 and Product 2 are changed to $405 and $135, respectively. Will the current optimal solution remain the same? g) Suppose that the unit profit for the Product 1 is fixed at $500. What is the range of unit profit for Product 2 that will keep the optimal solution unchanged

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