SOLUTION: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 85P –

Algebra ->  Equations -> SOLUTION: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 85P –       Log On


   



Question 1058958: A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to the price P, in dollars, of an oven by the function R(P) = 85P – 0.25P^2. What price will give the maximum revenue?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to
the price P, in dollars, of an oven by the function R(P) = 85P – 0.25P^2. What price will give the maximum revenue?
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They want you find the maximum of this quadratic function

R(P) = 85P+-+0.25P%5E2.

The general theory says that the quadratic function y(x) = ax%5E2+%2B+bx+%2B+c has the maximum/minimum at x = -b%2F2a,

which in your case is -85%2F%282%2A%28-0.25%29%29 = -85%2F%28-0.5%29 = 170 dollars.

Answer.  170 dollars.

There is a bunch of lessons in this site on finding the maximum/minimum of quadratic functions
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola