SOLUTION: 1. An event promoter in Belize is selling tickets to her all-inclusive Carnival fete for $150.00 each. She has rented a venue at a cost of $3500 and will incur other fixed costs fo

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Question 1197572: 1. An event promoter in Belize is selling tickets to her all-inclusive Carnival fete for $150.00 each. She has rented a venue at a cost of $3500 and will incur other fixed costs for a DJ ($1000), MC ($500), stage ($3,000), event staff ($4,000), insurance ($500), and marketing ($2,500). The variable costs include drinks ($30 per person), and food ($45 per person).
a) What is the revenue function for the event?
b) What is the cost function for the event?
c) Calculate how many tickets need to be sold in order for the event to break even.
d) If the promoter sells 500 tickets:
i. Calculate the revenue
ii. Calculate the cost
iii. Calculate the profit
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a) The revenue function is 150n, since the ticket costs $150 each.
b) The cost function is 15000%2B75n, which is the fixed cost (adds up to $15,000 total) plus the variable cost ($75 per person for the drinks and food)
c) In order for the event to break even, the revenue must equal the cost, so we have the equation 150n=15000%2B75n. Subtracting 75n from both sides, we get 75n=15000. Finally, dividing by 75, we get n=200 tickets.
i. The revenue is 150%2A500=75000 dollars.
ii. The cost is 15000%2B75%2A500=52500 dollars.
iii. The profit is the revenue minus the cost, so it is 75000-52500=22500 dollars.