SOLUTION: The owner of a sidewalk expresso stand that the weekly profit for their business is a function of the price they charge per cup. If x equals the price(in dollars) of one cup, the w

Algebra ->  Test -> SOLUTION: The owner of a sidewalk expresso stand that the weekly profit for their business is a function of the price they charge per cup. If x equals the price(in dollars) of one cup, the w      Log On


   



Question 194959: The owner of a sidewalk expresso stand that the weekly profit for their business is a function of the price they charge per cup. If x equals the price(in dollars) of one cup, the weekly profit is given by P(x) = -2900x^2+7250x -2900.
Approximate the maximum profit and the price per cup that produces that profit

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29+=+-2900x%5E2+%2B+7250x+-+2900
When an equation is of the form
ax%5E2+%2B+bx+%2B+c, the max or min
occurs where x+=+-b%2F%282a%29
In this case,
a+=+-2900
b+=+7250
The maximum (in this case) occurs at
x%5Bmax%5D+=+%28-7250%29+%2F+%282%2A%28-2900%29%29
x%5Bmax%5D+=+%28-7250%29+%2F+-5800
x%5Bmax%5D+=+5%2F4
The price per cup for maximum profit is $1.25
P%28max%29+=+-2900x%5E2+%2B+7250x+-+2900
P%28max%29+=+-2900%2A%285%2F4%29%5E2+%2B+7250%2A%285%2F4%29+-+2900
P%28max%29+=+-4531.25+%2B+9062.5+-+2900
P%5Bmax%5D+=+1631.25
The maximum profit is $1631.25
To check this answer, both $1.24 per cup
and $1.26 per cup should give a little
less profit.
For $1.26/cup, I get $1630.96