Model Management and Extreme Makeover In the model-management industry, firms supply human models for advertisements. Models vary in skin color, which is measured on a line of unit length. Skin color can be modified with makeup, and the makeup costs are incurred by the firm. Each firm enters the market at an address on the color line, and each firm manages two models. Suppose the cost of an extreme makeover (the cost of going from one end of the color line to the other) is $90. Illustrate the determination of makeup cost in (i) a city with 4 models (2 firms) and (ii) a city with 6 models (3 firms), including values for the makeup cost per model.

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?