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

Upper R left parenthesis x right parenthesis equals 79 x minus 0.2 x squared .R(x)=79x−0.2x2.

The monthly cost C of selling x wristwatches is Upper C left parenthesis x right parenthesis equals 32 x plus 1650.C(x)=32x+1650.

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

(b) Profit is given as

Upper P left parenthesis x right parenthesis equals Upper R left parenthesis x right parenthesis minus Upper C left parenthesis x right parenthesis .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.