<PRE><B>Question 142889</B>
Demand for pools.
Tropical pools sells an above ground model for p dollars each. The monthly revenue from the sale of this model is given by
R= -0.08p^2 +300p
Revenue is the product of the price p and the demand (quantity sold). 
a. Factor out the price on the right-hand side of the formula.
p(0.08p+300)
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b. What is an expression for the monthly demand?
D(p) = -0.08p+300
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c. What is the monthly demand for this pool when the price is $3,000.
D(3000) = -0.08*3000+300 = 60 units
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d. Use the graph to estimate the price at which the revenue is maximized.
{{{graph(400,300,-1500,5000,-105000,300050,-0.08x^2 + 300x)}}}
max occurs at p = -b/2a = -300/(2*-0.08) = $1875

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e. Approximately how many pools will be sold monthly at this price?
D(1875) = -0.08*1875+300 = 150 units
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e. What is the approximate maximum revenue?
R(p) = -0.08p^2 +300p
R(1875) = 0.08(1875)^2 + 300(1875) = $281,250
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Cheers,
Stan H.


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