1. A manufacturer has been selling 1000 television sets a week at $400 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week. Round your answers to the nearest dollar.
(a) Find the demand function (price as a function of units sold).
(b) How large a rebate should the company offer the buyer in order to maximize its revenue?
(c) If the company experiences a cost of C(x) = 68,000 + 130x, how should the manufacturer set the size of the rebate in order to maximize its profit?
2. An airline finds that if it prices a cross-country ticket at $200, it will sell 300 tickets per day. It estimates that each $10 price reduction will result in 50 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue.
Find the point of diminishing returns for the profit function where x is the amount spent on marketing in million dollars.
P(x) = 4x + 30x2 - 2.5x3; for 0 ≤ x ≤ 6.