Two machines are used to produce two types of products. A unit of Product 1 requires 2 hours of processing time on Machine 1, and 1 hour of processing time on Machine 2. A unit of Product 2 requires 1 hour of processing time on Machine 1, and 2 hours of processing time on Machine 2. Daily processing time available on each machine is 8 hours. Selling one unit of Product 1 will generate $300 net profit. Selling one unit of Product 2 will generate $200 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 $50 per hour? Why? e) Should you increase the availability of Machine 2 at an additional cost of $50 per hour? Why? f) Suppose that the unit profit for the Product 1 and Product 2 are changed to $350 and $250, respectively. Will the current optimal solution remain the same? g) Suppose that the unit profit for the Product 2 is fixed at $200. What is the range of unit profit for Product 1 that will keep the optimal solution unchanged