Maximizing profit?

Question

We give the cost C of producing x units of a particular commodity and the selling price p when x units are produced. Determine the level of production that maximizes profit.

 

C(x) =2/5 x²+9x+33 and p(x)=1/5 (93-x)

Answer 1

Revenue (R) = (Number of units sold)*(price per unit)

R = x*p(x) = -(1/5)x² + (95/3)x

 

Profit (P) = Revenue - Cost

P = -(1/5)x² + (95/3)x - (2/5)x² - 9x - 33

P = -(3/5)x² + (48/5)x - 33

 

To find the production (x) that maximizes profit, take the derivative of P wrt x, set it to zero, and solve for x.