The Better Baby Buggy Co. has just come out with a new model, the Turbo. The market research department predicts that the demand equation for Turbos is given by q = −4p + 616, where q is the number of buggies the company can sell in a month if the price is $p per buggy. At what price should it sell the buggies to get the largest revenue? p = $ What is the largest monthly revenue? $
Accepted Solution
A:
In this question, q is the number of buggies the company can sell in a month if the price is $p per buggy. The revenue should be number of buggies sold(q) multiplied by the price(p). The equation would be:
revenue= p * q revenue= p * (-4p + 616)= -4p^2 + 616p
The maximum revenue should be in the peak of the graph. The calculation would be: -4p^2 + 616p -4*2 p^2-1 + 616*1 p^1-1=0 -8p + 616=0 8p= 616 p=77
Put p=77 in the revenue equation would result revenue= -4p^2 + 616p revenue= -4(77^2) + 616(77) = -23716 + 47432= $23716