The Acme Heavy Equipment School teaches students how to drive construction machinery

The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that the school can educate per week is given by q ¼ 10 min(k, l) r , where k is the number of backhoes the firm rents per week, l is the number of instructors hired each week, and g is a parameter indicating the returns to scale in this production function. a. Explain why development of a profit-maximizing model here requires 0 < g < 1. b. Supposing g ¼ 0.5, calculate the firm’s total cost function and profit function. c. If v ¼ 1000, w ¼ 500, and P ¼ 600, how many students will Acme serve and what are its profits? d. If the price students are willing to pay rises to P ¼ 900, how much will profits change? e. Graph Acme’s supply curve for student slots, and show that the increase in profits calculated in part (d) can be plotted on that graph.