Solve the problem.
-The stadium vending company finds that sales of hot dogs average 48,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by
5000 hot dogs. What price per hot dog should the vending company charge to realize the maximum
Revenue?
A) $3.90
B) $2.30
C) $4.80
D) $3.65

Question

Quizplus · Accepted Answer

The revenue is given by the product of the price and the number of hot dogs sold. The number of hot dogs sold is a linear function of the price, with a slope of -5000/0.50 = -10000. The revenue is therefore a quadratic function of the price, with a maximum at the vertex. The vertex of a quadratic function with a negative leading coefficient is at the x-coordinate of -b/2a, where a and b are the coefficients of the quadratic. In this case, a = -10000 and b = 48000, so the vertex is at -48000/(-2*10000) = $3.65.

Solve the Problem. -The Stadium Vending Company Finds That Sales of Hot Dogs