The question is the following: YOur school has contracted with a professional magician to perform at the school. The school has guaranteed an attendance of at least 1000 and total ticket receipts of at least $4800. The tickets are $4 for students and $6 for non students, of which the magician receives $2.50 and $4.50 respectively. What is the minimum amount of money the magician could receive?

Question

I am unsure how to set this up. So far I have 1000 is greater than or equal to 4s+6n (S=student n=nonstudent).

Answer 1

I think i would look at this from another direction. the first part of the question says there is a guaranteed attendance and a guaranteed total ticket receipt. i would take this to mean that the magician is guaranteed a minimum of either 1000 attendees or $4800 which ever is greatest.

so... if 1000 students showed up, that would only be $4000 (the minimum for 1000 attendees), which would mean we should work with the greater which would be minimum receipts of $4800.

then... i know that of every $4 taken in, the magician gets $2.50, or 62.5%

thus... 0.625*4800=$3000

but, you have to check the assumptions we made in the beginning.

Answer 2

This is a "linear programming" question

first condition:
S + n > 1000

second condition:
4S + 6n > 4800 or
2S + 3n > 2400

now graph these in the first quadrant on a S n grid, use the intercepts and it will be easy
it is easy to solve S+n=1000 with 2S+3n=2400 to get
S=600 and n=400

The profit equation for the magician would be
Prof = 2.5S + 4.5n

check:
if S=600, n=400
Prof = 600(2.5) + 400(4.5) = 3300