Question

The stadium vending company finds that sales of hot dogs average 35,000 hot dogs per game when the hot dogs sell for $2.50 each. For each 25 cent increase in the price, the sales per game drop by 2000 hot dogs. Determine a function R x that models the total revenue per game, where x is the number of $0.25 increases in the price of a hot dog.

Answer 1

A function R x that models the total revenue per game is as follows:

Rx = 87,5000 + 3,750x – 500x^2.

Explanation:

Based on the information in the question, we have:

Rx = Total revenue per game

x = Number of $0.25 increases in the price of a hot dog

Average sales of hot dogs = 35,000

Effect of each 25 cent increase in the price on average sales = 35,000 - 2000x

Effect of each 25 cent increase in the price on selling price = 2.5 + 0.25x

Therefore, we have:

Rx = (35,000 - 2000x)(2.5 + 0.25x)

This can be solved further by opening the brackets as follows:

Rx = 87,5000 + 8,750x - 5,000x - 500x^2

Rx = 87,5000 + 3,750x – 500x^2

Therefore, a function R x that models the total revenue per game is Rx = 87,5000 + 3,750x – 500x^2.