|
Question 919163: An espresso stand finds that its weekly profit is a function of the price, x, it charges per cup. If x is in dollars, the weekly profit is P(x)=−3000x2+11400x−9252 dollars.
(a) What is the maximum weekly profit. $______ (Round to the nearest cent)
(b) What price per cup that produces that maximum profit? $ _____ (Round to the nearest cent.)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An espresso stand finds that its weekly profit is a function of the price, x, it charges per cup. If x is in dollars, the weekly profit is P(x)=−3000x2+11400x−9252 dollars.
(a) What is the maximum weekly profit. $______ (Round to the nearest cent)
(b) What price per cup that produces that maximum profit? $ _____ (Round to the nearest cent.)
***
P(x)=−3000x2+11400x−9252
complete the square:
P(x)=−3000(x^2-3.8x+(3.8/2)^2)+3000*(1.9)^2−9252
=-3000(x-1.9)^2+10830-9252
=-3000(x-1.9)^2+1578
This is an equation of a parabola that opens up with vertex at (1.9,1578)
(a) What is the maximum weekly profit? $1578
(b) What price per cup that produces that maximum profit? $1.90
|
|
|
| |
