Answer Happy

(10 points) A manufacturer has been selling 1200 QLED televisions a week at $360 each. A market survey indicates that for each $20 discount offered to a buyer, the total number sold will increase by 200 TVs per week. We will define the variable a to represent the number of $20 discounts that are offered. We will allow a to be any real number, including decimal values. (a) Find the function p(a) which gives the price of a television in dollars, where a is the number of discounts. p(a) = (b) Find the function q(a) which gives the quantity of televisions sold (the weekly demand), where a is the number of discounts. q(a) = (c) Find the total revenue function R(a) which gives the weekly revenue in dollars, where a is the number of discounts. R(a) = (d) Find the value of a that will maximize the weekly revenue function R(a). Do not round your answer. The value of a to maximize weekly revenue is a = (e) Use your answers above to complete the following sentences. Round each answer to the nearest whole dollar. In order to maximize weekly revenue from the sale of QLED televisions, the manufacturer should discount the current price by a total of $ . The new price will be $ which will generate a weekly revenue of $ (f) Still using the a variable defined above, now suppose the weekly cost in dollars is given by the function C(a) = 216000 + 24000a. Determine the value of a that will maximize the weekly profit. Do not round your answer. The value of a to maximize weekly profit is a = (g) Use your answers above to complete the following sentences. Round each answer to the nearest whole dollar. In order to maximize weekly profit from the sale of QLED televisions, the manufacturer should discount the current price by a total of $ The new price will be $ which will generate a weekly profit of $