A retail furniture shop can buy dining room chairs from a manufacturer for $40 each. The retailer knows that if each chair sells for $100, 50 of them can be sold per week. However the research department believes that for every $4 reduction in price they will sell 20 more chairs per week.
Suppose that n chairs are sold per week, that each chair sells for $x and that the total sales revenue is $R per week.
a) show that n=550 -5x
b) show that R= 550x -5x^2
c) show that the profit function, P(x) = 750x -5x^2 -22000