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IV. (30%) SmallCorp is capable of manufacturing three types of clothing shirts, shorts, and pants. The manufacture of each type of clothing requires that SmallCorp have the appropriate type of machinery available. The machinery needed to manufacture each type of clothing must be rented at the following rates: shirt machinery, $75 per week; shorts machinery, $50 per week; pants machinery, $100 per week. The manufacture of each type of clothing also requires the amounts of cloth and labor below. Each week, 750 hours of labor and 900 sq yd of cloth are available. The variable unit cost and selling price for each type of clothing are also shown below. Resource Requirements Revenue and Cost Information Clothing Labor Cloth Clothing Sales Variable Type Chours) (Square Venis) Type Price (8) Cost (5) Shirt 3 4 Shirt 12 6 Shorts 2 3 Shorts 8 4 Pants 6 Pants 15 a. (15%) Assume that SmallCorp, in a particular week, decides not to produce pants, but produce only 125 shirts and 130 shorts. (1) Is this solution feasible? Justify your answer. (ii) Compute the SmallCorp's weekly profit for this week. Clearly show your calculations. b. (15%) Assume that, in a particular week, SmallCorp must produce at least 50 pants, 50 shirts, and 50 shorts. How many shirts, shorts and pants must SmallCorp produce to maximize SmallCorp's weekly profit? Compute the SmallCorp's profit for this week