B. You manage a plant that mass-produces engines by teams of workers using assembly machines. The tech- norlogj,r is summarized by the production function q=5KL where at is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r = $10,000 per week, and each team costs to = $5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. a. What is the cost function for your plantnamely, how much would it cost to produce q engines? What are average and marginal costs for produc- ing q engines? How do average costs var},r with output? b. How many teams are required to produce 250 engines? What is the average cost per engine? c. You are asked to make recorrunendations for the design of a new production facility. What capital! labor (KIL) ratio should the new plant accommo- date 'Lf it wants to nunjmize the total cost of produc- ing at any level of output