Suppose that you own a manufacturing company which produces a particular good.

(a) Suppose that your company sells x units of a good at a price of $3. What is your revenue function?

(b) Suppose the marginal cost of production is $4 and that the total cost to produce 5 units of the good is $50. Assuming that costs are linear, what is your cost function?

(c) What are the fixed costs from your cost function in part (b)?

(d) Assume that you have a complete overhaul of your facility. As a result, you have new revenue and cost functions R(x) = x 2 + 9x and C(x) = 3x + 5. What is your break even quantity? (If there are multiple break even quantities, list all of them.)

(e) Using the revenue and cost functions from part (d), determine the number of units that should be sold in order to maximize your profit. What is the maximum profit?