A toy store owner estimates that by charging x dollars each for a certain toy, he can sell 40−x toys each week. The quadratic equation R=−x^2+40x is used to find the revenue, R , received when the selling price of a toy is x . Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

Accepted Solution

Answer:x=20Step-by-step explanation:Given selling Price of Toy is x dollarshe can sell 40-x toys each weekThus Revenue Generated from selling 40-x toys at x dollar can be given by [tex]R=-x^2+40x[/tex]To get maximum Revenue differentiate R with respect to x  and equate it to 0therefore [tex]\frac{\mathrm{d} R}{\mathrm{d} x}=-2x+40[/tex][tex]-2x+40=0[/tex][tex]x=20[/tex]thus for maximum Revenue owner sells 20 toys each weekMax Revenue [tex]R=-(20)^2+40\times 20=-400+800=$ 400[/tex]