The Clearvoice cell phone company is considering investing in additional cell phone towers across the country to improve its coverage and attract more customers. It estimates that if it builds K numbe

a. Clearvoice total cost when it builds K towers would be {eq}C(K) = 20K {/eq} million dollars. Each tower costs 20 million dollars, and the company is building K towers. Therefore, the total cost of building K towers would be 20K million dollars. b. Clearvoice marginal cost would be {eq}MC(K) = 20 {/eq} million dollars. Marginal cost is the change in total cost that occurs when an additional unit is produced. In this case, since each tower costs 20 million dollars, the marginal cost of building an additional tower would be 20 million dollars. c. Clearvoice should build {eq}250 {/eq} towers to maximize profit. To determine the optimal number of towers to build, we need to find the point where marginal benefit equals marginal cost. That is, {eq}MB(K) = MC(K)\ 500 -2K = 20\ 2K = 480\ K = 240 {/eq} However, since the company wants to build additional towers to improve coverage and attract more customers, it should build one more tower than the optimal number calculated above. Therefore, the company should build {eq}250 {/eq} towers. This ensures that the company has extra capacity to handle increased demand in the future.