SOLUTION: Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this model is given by the formula R(p)=-0.08p^2 + 300p. Revenue is the product of the pri

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Question 204002: Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula
R(p)=-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.
b) Write a formula D(p) for the monthly demand.
c) Find D(3000).
d) Use the accompanying graph to estimate the price at
which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?
e) What is the approximate maximum revenue?
f) Use the accompanying graph to estimate the price at
which the revenue is zero.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula
R(p)=-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(p) = p(-0.08p+300)
--------------------------------------
b) Write a formula D(p) for the monthly demand.
D(p) = -0.08p+300
--------------------------
c) Find D(3000)= -0.08*3000+300 = 60
--------------------------------
d) Use the accompanying graph to estimate the price at
which the revenue is maximized. Approximately how
many pools will be sold monthly at this price?
Max occurs when p = -b/2a = -300/(2*-0.08) = 1875
----------------------------
e) What is the approximate maximum revenue?
R(1875) = -0.08(1875)^2+300*1875 = $281,250
----------------------------
f) Use the accompanying graph to estimate the price at
which the revenue is zero.
Comment: No graph appeared in your post.
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Cheers,
Stan H.