The monthly revenue R achieved by selling x wristwatches is figured to be

Upper R left parenthesis x right parenthesis equals 71 x minus 0.2 x squared . The monthly cost C of selling x wristwatches is Upper C left parenthesis x right parenthesis equals 28 x plus 1700.

(a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue?

(b) Profit is given as P(x) = R(x)- C(x) . What is the profit function?

(c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit?

(d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue.