SOLUTION: this is a word problom from my college algebra I book that deals with Inverse Functions: "John owns a hotdog stand. He has found that his profit is represented by the equation P=-x

Algebra ->  Functions -> SOLUTION: this is a word problom from my college algebra I book that deals with Inverse Functions: "John owns a hotdog stand. He has found that his profit is represented by the equation P=-x      Log On


   

Question 533657: this is a word problom from my college algebra I book that deals with Inverse Functions: "John owns a hotdog stand. He has found that his profit is represented by the equation P=-x^2+56x+77, with P being profits and x the number of hotdogs. How many hotdogs must he sell to earn the most profit? What will be his maximum profit?"
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
P+=+-x%5E2%2B56x%2B77 This is a quadratic equation which, when graph, will give a parabola that opens downward. (Note the negative x%5E2 term)
The x-coordinate of the maximum of this parabola, and thus the maximum number of hotdogs, is given by:
x+=+-b%2F2a where: a = -1 and b = 56, so...
x+=+-56%2F2%28-1%29
x+=+28
John must sell 28 hotdogs to earn the most profit.
The maximum profit, P%5Bm%5D, can be found by substituting x+=+28 into the given equation for profit.
P%5Bm%5D+=+-%2828%29%5E2%2B56%2828%29%2B77
P+=+861