4. The owner of a local amusement park needs to identify the optimum price for admission tickets to maximize his profits. The number, N, of people who attend the amusement park is a function of the price, p, in dollars. N(p) = (p+5)(p 17), assuming the minimum ticket price is $12.00. The revenue generated, R, in dollars is R(p) = N(p) x p, where p is the number of tickets sold. The cost, C, of running the amusement park can be modelled by a composite function of N(p), C(p) = 75 + 12N(p) a. Graph this function, C(p) using desmos.org Paste a screenshot of the graph below.
4. The owner of a local amusement park needs to identify the optimum price for admission tickets to maximize his profits. The number, N, of people who attend the amusement park is a function of the price, p, in dollars. N(p) = (p+5)(p 17), assuming the minimum ticket price is $12.00. The revenue generated, R, in dollars is R(p) = N(p) x p, where p is the number of tickets sold. The cost, C, of running the amusement park can be modelled by a composite function of N(p), C(p) = 75 + 12N(p) a. Graph this function, C(p) using desmos.org Paste a screenshot of the graph below.
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 44PS: A company determines that its weekly profit from manufacturing and selling x units of a certain item...
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Transcribed Image Text:4. The owner of a local amusement park needs to identify the
optimum price for admission tickets to maximize his profits. The
number, N, of people who attend the amusement park is a
function of the price, p, in dollars. N(p) = (p+5)(p - 17),
assuming the minimum ticket price is $12.00. The revenue
generated, R, in dollars is R(p) = N(p) x p, where p is the number
of tickets sold. The cost, C, of running the amusement park can be
modelled by a composite function of N(p), C(p) = 75 + 12N(p)
a. Graph this function, C(p) using desmos.org Paste a
screenshot of the graph below.
Transcribed Image Text:b. Graph the combined function y = R(p) - C(p) using
desmos. Paste a screenshot below. What does this function
represent?
c. Identify the region for which R(p) - C(p) > 0. What is the
significance of this region?
d. Do the maxima of y = R(p) and y = R(p) - C(p) occur for
the same value of p? Explain why or why not.
e. Identify the optimum ticket price for the amusement park
and determine the maximum profit per ticket.
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