A retailer wishes to price a toy car which has a wholesale cost to him of $5 per car, so as to maximize his total profit. Experience has shown that if he charges x dollars per car, he will be able to sell 200 - 20x cars.
a) Find the total revenue, R(x), when the selling price per car is x dollars.
b) Find the profit per car when the selling price is x dollars.
c) Find the total profit, P(x), when the selling price is x dollars.
d) Graph the profit and revenue functions over an appropriate range of values for x.
e) Find the maximum profit, the selling price per car necessary to achieve it and the number of cars sold to achieve maximum profit.