A cell phone company is considering investing in additional cell phone towers to improve its coverage and attract more customers. Total benefit is 200K - 2K^2 million dollars and each tower (K) costs 25 million dollars.
a) What are the marginal benefit, total benefit, marginal cost, total cost, and profit when it builds K towers? Treating its investment as finely divisible, how many cell towers should it build?
b) Now each tower costs 50 million dollars, how many cell towers should it build?