5. In each case describe the rm's prot maximizing output when P = 100, when P : 200, when P : 300, and when P : 400 and graph the rm's supply. Assume the rm is in a perfectly competitive market the rm's output does not impact the price and the rm has no control over price. (a) The rm has a xed cost of $100,000, a total cost of C(q) : $100, 000 + 100Q + 056?, and a marginal cost of 100 + .162. Hint: Producing where P : MC maximizes prot. (b) The rm has a xed cost of $100,000, at total cost 0100;!) : $100, 000 + 15062, a marginal cost equal to 150, and it can produce any output up to 1000. Hint: it is not possible to solve for the quantity that makes P : MC, so answer this intuitively. The answer may not seem very realistic to you, but then the cost function isn't realistic. (c) The rm has a xed cost of $100,000| per plant and a total cost of C(q} : $100, 000 + 15062 for each plant where Q is the output at each plant, and it can product output up to 1000 per plant. The rm can build 0, 1, 2, or 3 plants. Hint: each plants will produce 1000 units if it is built, and if building one plant is protable, building three plants will be three times as protable