SOLUTION: CAN SOMEONE HELP ME WITH THIS QUESTION. Demand for pools. Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this model is given by the form

Algebra ->  Functions -> SOLUTION: CAN SOMEONE HELP ME WITH THIS QUESTION. Demand for pools. Tropical Pools sells an aboveground model for p dollars each. The monthly revenue for this model is given by the form      Log On


   

Question 201171This question is from textbook Elementary and Intermediate Algebra
: CAN SOMEONE HELP ME WITH THIS QUESTION.
Demand for pools. Tropical Pools sells an aboveground
model for p dollars each. The monthly revenue for this
model is given by the formula
R(p)= -0.08p2 + 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.
 This question is from textbook Elementary and Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)


R%28p%29=-0.08p%5E2%2B300p Start with the given equation.


R%28p%29=p%28-0.08p%2B300%29 Factor out the GCF "p" (the price)


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b)

Recall that

Revenue = Price * Demand


Since "p" is the price, this means by elimination that the demand is -0.08p%2B300


So D%28p%29=-0.08p%2B300


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c)

D%28p%29=-0.08p%2B300 Start with the given equation.


D%283000%29=-0.08%283000%29%2B300 Plug in p=3000


D%283000%29=-240%2B300 Multiply


D%283000%29=60 Combine like terms.

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d)

The graph of the revenue function R%28p%29=-0.08p%5E2%2B300p is




From the graph (use the trace feature), we see that the maximum is at the point (1875, 281250)


So this means that the max revenue of $281,250 will be obtained when the price is $1,875.


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e)

The maximum revenue is $281,250 (see part d)


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f)

Using the graph, the revenue is zero when either the price is $0 or $3,750