SOLUTION: A new media platform, JP Productions, uses a model to discover the maximum profit it can make with advertising. The company makes a $6,000 profit when the platform uses 100 or 20

Question 1202410: A new media platform, JP Productions, uses a model to discover the maximum profit
it can make with advertising. The company makes a $6,000 profit when the
platform uses 100 or 200 minutes a day on advertisement. The maximum profit
of $10,000, can occur when 150 minutes of a day’s platform is used on
advertisements. Which of the following functions represents profit, PP(mm), where mm
is the number of minutes the platform uses on advertisement?
A P(m) = −0.064(x + 150^2 − 10000
B P(m) = −1.6(x − 150)^2 + 10000
C P(m) = −(x − 1000)(x − 6000)
D P(m) = −(x − 100)(x − 200)
Answer by ikleyn(52782) (Show Source): You can put this solution on YOUR website!
.


(A)  Formula (A) is written incorrectly,
     so we will not discuss it.



(B)  Formula (B) correctly describes the given information,
     giving the maximum value of $10000 at x= 150 minutes

     and giving correct values of $6000 at x= 100 minutes and x= 200  minutes.



(C)  Formula (C) gives the maximum half-way between the roots 1000 and 6000, i.e. at x= 3500,
     which is not the case.  So, formula (C) does not work.



(D)  Formula (D) gives the maximum half-way between the roots 100 and 200, i.e. at x= 150,
     which is good; but it gives the zero values at x= 100 and x= 200 minutes,
     which is not consistent with the given info.


ANSWER.  Only formula (B) is consistent with the description.

Solved.

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