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slava [35]
3 years ago
8

A model for a company's revenue from selling a software package is R(p) = -2.5p² + 500p, where p is the price in dollars of the

software. What price will maximize revenue? Find the maximum revenue.
The price $_____ maximizes the revenue.
The maximum revenue is $_____.
Mathematics
2 answers:
Leokris [45]3 years ago
8 0

Answer: p = $100,  R = $25,000

<u>Step-by-step explanation:</u>

The maximum is the y-value of the Vertex.

<u>Step 1: </u>Use the Axis-Of-Symmetry (AOS) formula to find x: x=\dfrac{-b}{2a}

R(p) = -2.5p² + 500p

        a=-2.5  b=500

p=\dfrac{-(500)}{2(-2.5)}

   =\dfrac{-500}{-5}

   =100


<u>Step 2</u>: Find the maximum by plugging the p-value (above) into the given equation.

R(100) = -2.5(100)² + 500(100)

          = -25,000 + 50,000

          = 25,000

stealth61 [152]3 years ago
7 0

It's a quadratic function

f(x)=ax^2+bx+c

If a < 0, then the function has a maximum value in vertex.

The vertex (h, k), where:

h=\dfrac{-b}{2a},\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}

We have:

R(p)=-2.5p^2+500p\\\\a=-2.5

Substitute:

h=\dfrac{-500}{2(-2.5)}=\dfrac{-500}{-5}=100\\\\k=R(100)=-2.5(100)^2+500(100)\\\\k=-2.5(10,000)+50,000\\\\k=-25,000+50,000\\\\k=25,000

<h3>Answer:</h3><h3>The price $100 maximizes the revenue.</h3><h3>The maximum revenue is $25,000.</h3>
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