Question 930645: 4. A model for a company's revenue from selling a software package is R = -2.5p2 + 500p, where p is the price in dollars of the software.
a. What price will maximize the revenue? Give a reason for your answer.
b. What is the maximum revenue? Give a reason for your answer.
Found 2 solutions by TimothyLamb, ewatrrr:
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! R = -2.5p2 + 500p
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substitute p with x
set R = 0
-2.5xx + 500x = 0
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the above quadratic equation is in standard form, with a=-2.5, b=500 and c=0
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-2.5 500 0
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has a maximum at = ( 100, 25000 )
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answer:
price for maximum revenue = $100
this is the p (or x) coordinate of the equation's maximum
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maximum revenue = $25,000
this is the R (or y) coordinate of the equation's maximum
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Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website! R = -2.5p2 + 500p
Note: 500/-(-2*2.5) = 100
R = -2.5(p -100)^2 + 25, 000 Parabola opening downward V(100,25,000)
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a) p = $100 will maximize the revenue. V(100,25000)max
b) max R = $25,000 . V(100,25000)max
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