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.
R= - 0.08p^2 + 300p = p ( -0.08p + 300)
B) What is an expression for the monthly demand?
since revenue is price times demand, then the demand is:
-0.08p + 300
C) What is the monthly demand for this pool when the price is $3000?
demand= -0.08(3000) + 300 = 60
D) Estimate the price at which the revenue is maximized. Approximately how many pools will be sold monthly at this price?
the maximum of the revenue occurs when R'= -2(0.08)p+300 =0
i.e when p= 300/2(0.08) = 1875.
E) what is the approximate maximum revenue?
R=-0.08(1875)^2 + 300(1875) = 281 250.00.
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