SOLUTION: 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 dol
Algebra.Com
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
RELATED QUESTIONS
Hello! I need some help trying to solve parts a and b. I've already used the quadratic... (answered by stanbon)
P(x) = -560x^2 + 5488x - 2695
where P(x) is the weekly profit in dollars when the price... (answered by ewatrrr)
The owner of a sidewalk expresso stand find that the weekly profit for their business is... (answered by josmiceli)
The owner of a sidewalk expresso stand that the weekly profit for their business is a... (answered by josmiceli)
A community bird-watching society makes and sells simple bird feeders to raise money for... (answered by ikleyn)
A company has determined that its weekly profit is a function of the number of items that (answered by Timnewman)
A community bird-watching society makes and sells simple bird feeders to raise money for... (answered by drcole)
Market research suggests that if a particular item is priced at x dollars, then the... (answered by Boreal)
1) A manufacture has been selling 1650 television sets a week at $540 each. A market... (answered by Theo)