Question

A model of the daily profits p of a gas station based on the price per gallon g is p = -15,000g2 + 34,500g – 16,800.

How much money did the company invest in gas?
Find the price that will yield the maximum profit.
What is the maximum profit?
What is the lowest price of gas needed to break even?

Answer 1

Explanation:

P = -15000g² + 34,500g - 16800

use quadratic formula to find the 2 solutions for g when P = 0

(a=-15,000, b=34500, c=-16800)

g= 0.7, g=1.6

1) company invested $16,800

2) price that yields max. p = (0.7 + 1.6)/2 = $1.15

3) max. P = -15,000(1.15)² + 34,500(1.15) - 16,800 = $3037.50

4) lowest price to break even = $0.70