Linear Programming\r\n\r\nPillercat, Inc. produces several types of heavy equipment. Two of its products, the R-1 and the R-2, are produced in the same departments with the same equipment. Management must recommend the quantities of R1 and R2 to produce in May, based on the following information:\r\n1. Pillercat\\\'s marketing manager has judged that at current market prices, the firm cannot sell more than 12 R-1\\\'s and 12 R-2\\\'s per month.\r\n2. Contribution margins are $10,000 for each R-1 and $8,000 for each R-2.\r\n3. There are two production departments, A and B. Each R-1 uses 10 hours of machining in Dept. A and 20 hours of machining in Dept. B. Each R-2 uses 15 hours of machining in Dept. A and 10 hours in Dept. B. Total machining hours available during the month are 150 in Dept. A and 160 in Dept. B.\r\n4. Quality testing is performed in a third department. Each R-1 receives 30 hours of testing, and each R-2 receives 10 hours of testing. Total testing hours available are 175. \r\n5. In order to maintain the current market position, top management has decided that it is necessary to produce at least two R-2s for every R-1 produced.\r\n6. A major customer has ordered a total of five R-1\\\'s and R-2\\\'s (in any combination; for example 4 R-1\\\'s and 1 R-2, or 2 R-1\\\'s and 3 R-2\\\'s, etc.) for next month. So a total of at least 5 machines must be produced. \r\n\r\nRequirement 1\r\n\r\n1. What are the optimal production quantities of R1 and R2 for May? Use Solver as we did in class for Problem 11-40. Non-integer solutions--for example, 5.4 R-1\\\'s--are okay. (The firm can start a unit and get 40% of the way through the production process in May, and finish it in June.)\r\n2. What is the total contribution margin if this product mix is produced and sold?\r\n3. Why should Pillercat produce more R2s when R1 has a higher unit contribution margin? (Don\\\'t just say, \\\"Because this yields a higher total profit.\\\" Explain in terms of the production process and/or customer demand. If both production and demand are relevant, then include both in your explanation.) \r\n\r\nRequirement 2\r\n\r\nMarket demand is higher than Pillercat\\\'s optimal production quantities in Requirement 1. If the Pillercat expands its production facilities, then perhaps it could make a higher profit. Suppose that adding 50 hours of capacity in any one or more of the three departments--A, B, or Quality--would add $5,000 to monthly fixed costs. \r\nManagement is deciding whether or not to add 50 hours of capacity to Department A, Department B, Quality Testing, or split the 50 hours such that A would get 20 hours and B and Quality would each get 15 hours. \r\n\r\n\r\n1. Should Pillercat add the 50 hours of capacity? \r\n2. If yes, then should it add the 50 hours to A, B, Quality, or split the 50 hours among the three departments? \r\n3. In terms of customer demand and/or production efficiency, why is the choice you made in question 2 the most profitable?