In Exercise 10 of the Chapter 2 Review, we found that the relationship between price and demand (number of items sold) for Pomelia’s decorative lawn sprinkler business was given by p(x) =–1.25x + 85, where x was the number of items sold and p was the price per item. Since revenue (the money resulting from sales) is found by the product
(number of items) × (price per item) = x× p(x),
we see that the revenue is a quadratic function of the number of items sold.
a. Find a quadratic function R(x) giving revenue as a function of x, the number of sprinklers sold per month.
r (seconds)
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
H (feet)
3.0213
4.0944
4.8326
5.2575
5.3764
5.1675
4.6634
3.8603
2.7728
b. How many sprinklers must be sold in order to maximize monthly revenue?
c. What is the maximum monthly revenue?
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