Suppose a tour guide has a bus that holds a maximum of 90 people. Assume his profit (in dollars) for taking n people on a city tour is P(n) = n(45 - 0.5n) -90. (Although P is defined only for positive integers, treat it as a continuous function.) a. How many people should the guide take on a tour to maximize the profit? b. Suppose the bus holds a maximum of 38 people. How many people should be taken on a tour to maximize the profit? a. Find the derivative of the given function P(n). P'(n) =]A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below. p = 600 - 0.5x and C(x) = 15,000 + 135x . . . (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce phones each week at a price of $ (Round to the nearest cent as needed.)X A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72,000 + 60x and p(x) = 300 - 30 . 0 s x = 9000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set? (A) The maximum revenue is $ (Type an integer or a decimal.)