Question 442009: Hello! I need some help trying to solve parts a and b. I've already used the quadratic formula to find the two zeros (.5 and 2) but I am having trouble moving forward. Thank you so much!!
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) = -2900x^2 + 7250x - 2900 dollars.
a) Approximate the maximum profit and the price per cup that produces that profit.
b) Which function, P(x - 2) or P(x) - 2, gives a function that has the same maximum profit? What price per cup produces that maximum profit?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Hello! I need some help trying to solve parts a and b. I've already used the quadratic formula to find the two zeros (.5 and 2) but I am having trouble moving forward. Thank you so much!!
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) = -2900x^2 + 7250x - 2900 dollars.
--
Note that value is the average of 0.5 and 2: (0.5+2)/2 = 1.25
--------------------------------------------------------------------
a) Approximate the maximum profit and the price per cup that produces that profit.
Maximum for a quadratic always where x = -b/2a = -7250/(2(-2900)) = $1.25
Then max profit = f(1.25) = $1631.30
---------------------------------
b) Which function, P(x - 2) or P(x) - 2, gives a function that has the same maximum profit? What price per cup produces that maximum profit?
---
P(x-2) moves all point 2 to the right and changes the price to x = $3.25.
=====================
Cheers,
Stan H.
|
|
|
