Answer to Question #30852 in Linear Algebra for Melissa

Question

To raise funds for its community activities, a Lions club is negotiating with int. carnivals to bring its midway to town for a 3 day opening. The event will be on a shopping Center lot which is to receive 10% of the gross revenue. The lions club will sell the tickets on site. Int. carnivals requires either $15000 plus 30% of revenue or $10000 plus 50% of revenue. Other towns had an average of $10 spent per customer. A) what is the break even attendance under each basis for remunerating int. carnivals? B) for each alternative, what will be the Colin's profit or loss if the attendance is I)3000 or ii) 2200?
C) how would you briefly explain the advantages and disadvantages of the two alternatives to a club member?

Answer 1

A)
1)For the first basis the equality of breakeven attendance will be:
$10*X = $15000 + 0.3*($10*X)
7X = 15000
X = 2143 tickets is the breakeven attendance
2) For the second basis the equality of breakeven attendance will be:
$10*X = $10000 + 0.5*($10*X)
5X = 10000
X = 2000 tickets is the breakeven attendance

B)
1) If the attendance is 3000 for the first case, then Profit = 10$*3000 - 0.3*(10$*3000) - 15000 = $6000
If the attendance is 2200 for the first case, then Profit = 10$*2200 - 0.3*(10$*2200) - 15000 = $400
2) If the attendance is 3000 for the second case, then Profit = 10$*3000 - 0.5*(10$*3000) - 10000 = $5000
If the attendance is 2200 for the second case, then Profit = 10$*2200 - 0.5*(10$*2200) - 10000 = $1000

C) So, we can see, that the first alternative gives higher profits, when the attendance is higher, but it should be not less than 2143 members. But if there are more than 2000 and less than 3000 members, the second alternative will gain the comparatively higher profit.