Need Steps and Explanations:

Suppose you manage a plant that produces engines by teams of workers using assembly machines. The technology is summarized by the production function q = 5LK, where q is the number of engines produced per week, L is the number of work teams hired, and K is the number of machines rented. Each team of workers costs $5,000 per week, and each machine rents for $10,000 per week. The cost of producing an engine is determined by the costs of labor and capital, plus $2,000 per engine for parts. a) If your current plant's capital is fixed at 5 machines, what is the plant's short run cost function of the form C = f(q)? b) What is the average cost function? C) If you receive a contract to produce 250 engines in one week, how many work teams (labor) will you need? d) What will be the average cost per engine? e) If you were designing a new facility, what capital to labor ratio (K/L) would you want to have