Question 320043
Demand for pools. Tropical Pools sells an above ground model for p dollars each. 
The monthly revenue for this model is given by the formula
R(p)= -0.08p^2 + 300p.
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Revenue is the product of the price p and the demand(quantity sold).
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a) Factor out the price on the right-hand side of the formula.
R(p)= p(-0.08p + 300).
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b) Write a formula D(p) for the monthly demand.
Demand is equal the revenue divided by the price
D(p) = {{{p(-.08p + 300)/p}}}
cancel p;
D(p) = -.08p + 300
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c) Find D(3000).
D(3000) = -.08(3000) + 300
D(3000) = -240 + 300
D(3000) = 60 pools when the price is $3000
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d) Use the accompanying graph to estimate the price at
which the revenue is maximized.
{{{ graph( 300, 200, -1000, 5000, -50000, 400000, -.08x^2+300x) }}} 
$1900 price for max revenue
:
 Approximately how many pools will be sold monthly at this price?
28000/1850 = 147 pools sold
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e) What is the approximate maximum revenue?
$280,000
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f) Use the accompanying graph to estimate the price at which the revenue is zero
$3800
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