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**Tessarina** 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