(i) A liquid form of a drug manufactured by a pharmaceutical firm is sold in bulk at a price of $200 per unit. If the total production cost (in dollars) for x units is C(x) = 500,000 + 80x + 0.003x2 If it is known that the production capacity of the firm is at most 30,000 units in a specified time. (a) What is the average cost function (b) What is the marginal average cost function (c) How many units of the drug must be manufactured and sold in that time to maximize the profit? (d) Would it benefit the pharmaceutical firm to expand the production capacity? Show why by illustrating your reason.

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