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Mathematics 25 Online
OpenStudy (anonymous):

Marge is planning a casino trip.If 100 people sign up, the cost is $300 per person. For each add. person above 100, the cost per person is reduced by $2 per person. To max. Marge's revenue, how many people should go on the trip? What is the cost per person? (Calculus)

OpenStudy (anonymous):

PLEASE HELP!

OpenStudy (valpey):

If 250 people sign up, what is the cost per person?

OpenStudy (valpey):

No. Marge's revenue is equal to the number of people times the cost per person. We know that when there are 100 people the cost per person is $300. The revenue at 100 people is 100*$300=$30,000. Let x be number of people, total revenue be r(x), and cost per person be c(x) then: \[r(x) = x*c(x)\]

OpenStudy (valpey):

But c(x) goes down by 2 for each additional person (above 100) so \[c^{\prime}(x) = -$2\text{ per additional person}\]

OpenStudy (valpey):

Therefore we can say: \[c(x) = -$2*x+C\] for some constant C. What does C need to be for c(100) = $300?

OpenStudy (valpey):

No. \[c(x)=$500-$2x\] \[r(x)=x($500-$2x)=$500x-$2x^2\] \[r^{\prime}(x)=$500-$4x\] If we want the local max, we should set r' equal to 0 or: \[$500=$4x\]

OpenStudy (valpey):

The number of people should be above 100 and below 250.

OpenStudy (anonymous):

I figured it out it is 125 people at $250 per person

OpenStudy (valpey):

Sweet. Well done.

OpenStudy (anonymous):

is this a calculus question?

OpenStudy (valpey):

The asker wrote "(Calculus)" but obviously, we don't have to think of it that way.

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