SOLUTION: Solve the problem. The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)=-5p(squared)+1330p when the unit price is p dollars. If the manufacturer

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the problem. The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)=-5p(squared)+1330p when the unit price is p dollars. If the manufacturer       Log On


   



Question 824418: Solve the problem.
The manufacturer of a CD player has found that the revenue R (in dollars) is
R(p)=-5p(squared)+1330p when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The manufacturer of a CD player has found that the revenue R (in dollars) is
R(p)=-5p(squared)+1330p when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?
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To find maximum R(p)
1. Find the vertex of R(p)
OR
2. Find and solve the derivative of R(p) ; if you know calculus.
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Find the vertex::
Max occurs when p = -b/(2a) = -1330/(2(-5)) = 133
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Max Revenue = R(133) = $88445
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Cheers,
Stan H.
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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
R%28p%29=-5p%5E2%2B1330p
'
-5p%5E2%2B1330p=0 will have a maximum.
For this maximum,
p=%28-1330%2B-+sqrt%281330%5E2-4%2A%28-5%29%2A0%29%29%2F%282%2A%28-5%29%29
p=%28-1330%2B-+sqrt%281330%29%29%2F%28-10%29
p=133%2B-+%281%2F10%29sqrt%281330%29
'
Looking at the middle of the two possible p values,
p=133%2F2 is where the maximum revenue should be.

highlight%28R%28133%2F2%29=-5%2A%28133%2F2%29%5E2%2B1330%28133%2F2%29%29, maximum revenue.