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)
PLEASE HELP!
If 250 people sign up, what is the cost per person?
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: \[r(x) = x*c(x)\]
But c(x) goes down by 2 for each additional person (above 100) so \[c^{\prime}(x) = -$2\text{ per additional person}\]
Therefore we can say: \[c(x) = -$2*x+C\] for some constant C. What does C need to be for c(100) = $300?
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: \[$500=$4x\]
The number of people should be above 100 and below 250.
I figured it out it is 125 people at $250 per person
Sweet. Well done.
is this a calculus question?
The asker wrote "(Calculus)" but obviously, we don't have to think of it that way.
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