3. A farm equipment firm produces small tractors at an estimated total cost: C = 37,500,000 + 5,000Q + 1.5Q2, where Q denotes annual tractor output. Regional demand for small tractors is given by: P = 30,000 – Q.  

a. Determine the firm’s profit maximizing output and price and its annual profit from tractors.  

b. Because of increased foreign competition, the demand for the firm’s tractors falls permanently to: P = 20,000 – Q. The firm is considering closing its plant immediately. By doing so, it can probably save $18 million of its annual $37.5 million in fixed costs. Alternatively, it can continue to operate the plant for 12 months after which if it shuts down it can suspend its contracts and plant lease and incur no continuing costs. Recommend its most profitable operating strategy and justify.