In this module, it is demonstrated that sometimes extensive diseconomies of scale, say, due to high transportation costs, would require that the firm produce its product in a multiple of plants. Suppose a beer brewing company has determined that its total production cost is TC= 1000Q-1.2Q^2 +0.004Q^3 where Q is its annual output measured in metric tons.

A. The average hauling (freight) cost is $0.8Q; that is AFC=0.8Q. Write the firm's average aggregated cost equation.

B. Now suppose the firm is facing the following market demand: Q=760,000-10P
Determine the optimal number of plants that the firm should have to take full advantage of the market demand.

C. Calculate the firm's profit.

For 5 extra bonus points:

D. Compare the firm's profit with multiple plants with its profit with a single plant.

Hint: The firms MC equation based on its aggregated total cost (including the freight cost) is MC=1000-0.8Q+0.012Q^2