(a) revenue-cost = profit
y = p(-(p+5)(p-17)) - (75+12(-(p+5)(p-17)))
= -(p^3-24p^2+59p+1095)
(b) R>C means P>0
The roots are at -5.2, 13.1, 16.1
From what you know about the shape of cubics, P>0 in the interval (13.1,16.1)
(c)
y' = -(3p^2-48p+59)
y' = 0 at p=14.65
y(14.65) = 47.37
Could someone please help me answer this question i am stuck!
A Marketing company provides the following formulas to the owner of an amusement park to help him make decisions about the park.
-The number , N, of people who attend the park is a function of price, p, in dollars:
N(p)=-(p+5)(p-17) assuming the minimum ticket price is $12.
- The revenue, R, is R(p)=N(p)multiplied by p
- The cost,C, of running the amusement park can be modelled by the function C(P)=75+12N(p)
a) write the combined function y=R(p)-C(p) and explain what it represents
b) Determine the interval(s) for p for which R(p)>C(p)
c)Identify the optimum ticket price for the amusement park and determine the maximum profit per ticket.
*for question b) and c) technology can be used to support the answer.
Thank you
3 answers
is there any other way to find the maximum profit
a graphical or numerical method would do the trick, if you don't have calculus to help.
1 answer