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? $

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