Question 967155: A food truck sells 500 sandwiches per day when they charge $9 per sandwich. It sells 100 more sandwiches per day for each $1 decrease in price. What price should the vendor charge to maximize the profit? What would be the maximum profit?
My Work:
let x = number of money decrease
let y = profit
y=500+9x
y=9-1x
y=(500+9x)(9-x)
y=4500-9x^2-500x+81x
y=(-9x^2)-419x+4500
I tried to solve using quadratic formula but my answer was way too large of a number. What did I do wrong?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Your first equation is wrong. Profit means revenue minus cost.
First, try to examine revenue and cost, either separately or together.
Examining your description further, you have no way to know about profit because you have no cost information.
x, Money Decrease________Price_________count__________Revnu_________
0________________________9_____________500
1________________________8_____________500+1*100
2________________________7___________500+2*100
3______________________9-3___________500+3*100
x______________________9-x___________500+100x_______(9-x)(500+100x)
You have now the function for revenue, using input, independant variable, x, the number of dollar decrease from $9.
Further factoring would be useful:
 ;
you should be able to find the roots and know how to handle the rest of the solution. Recall, this is only for revenue because your problem description gives nothing about cost.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website! A food truck sells 500 sandwiches per day when they charge $9 per sandwich. It sells 100 more sandwiches per day for each $1 decrease in price. What price should the vendor charge to maximize the profit? What would be the maximum profit?
My Work:
let x = number of money decrease
let y = profit
y=500+9x
y=9-1x
y=(500+9x)(9-x)
y=4500-9x^2-500x+81x
y=(-9x^2)-419x+4500
I tried to solve using quadratic formula but my answer was way too large of a number. What did I do wrong?
One of your binomials should be: 500 + 100x, not 500 + 9x
You should then get: f(x) = (500 + 100x)(9 - x), and subsequently, maximum profit of: 
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