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August 30th, 2010, 07:46 AM   #1
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I need help with maximizing profits problem

The Brick Oven Bakery sells more loaves of bread when it reduces its price, but then its profits change. The function y= -100(x-1.75)^2 + 300 models the bakery's profit, in dollars, where x is the price of a loaf of bread in dollars.

a. What price should the bakery charge to maximize its profits?

b. What is the maximum profit?

I can't figure out how to solve this problem; can someone help me? Help would be greatly appreciated. : )
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August 30th, 2010, 08:23 AM   #2
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Re: I need help with maximizing profits problem

You are conveniently given the parabolic profit function in the form

P = a(x - h) + k

Since a < 0, the vertex will be the upper bound of the function's range, or global maximum.

Use the fact that the vertex of the parabola is at (h,k) to find the price which maximizes profit and what that profit is.
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August 30th, 2010, 09:52 AM   #3
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Re: I need help with maximizing profits problem

So if I have to find the vertex I have to find the "x" (or h) value first correct? So to find that it's h= -b/2a right? Then I take that number and plug it into the equation to get the "y" value(or rather "k"), right? That's how you normally get the vertex, but don't I already have an h,k value (-1.75, 300)? I'm sorry, I'm still a bit confused.

EDIT: haha never mind I get it now, wow I can't believe I didn't realize the answer was right there! Thank you very much!
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