SOLUTION: Brooklyn has a summer window washing business. Based on experience Brooklyn knows that P= - 2x² + 130x - 1500 models her profit, P, in dollars, where x is the amount she charg
Question 1203125: Brooklyn has a summer window washing business. Based on experience Brooklyn knows that P= - 2x² + 130x - 1500 models her profit, P, in dollars, where x is the amount she charges per window. How much must Brooklyn charge to maximize her profit? What is the maximum profit?
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Brooklyn has a summer window washing business. Based on experience
Brooklyn knows that P= - 2x² + 130x - 1500 models her profit, P, in dollars,
where x is the amount she charges per window.
(a) How much must Brooklyn charge to maximize her profit?
(b) What is the maximum profit?
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They want you find the maximum of the quadratic function P(x) = -2x^2 + 130x - 1500.
It is well known fact that a quadratic function f(x) = ax^2 + bx + c gets its maximum value at
= .
In your case, a= -2, b= 130, therefore, = = = 32.50 dollars.
The maximum profit is then P(32.50) = -2*32.50^2 + 130*32.50 - 1500 = 612.50 dollars.
ANSWER. (a) $32.50; (b) $612.50.
