Question 1197572
a) The revenue function is {{{150n}}}, since the ticket costs $150 each.
b) The cost function is {{{15000+75n}}}, 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+75n}}}. Subtracting {{{75n}}} from both sides, we get {{{75n=15000}}}. Finally, dividing by 75, we get {{{n=200}}} tickets.
i. The revenue is {{{150*500=75000}}} dollars.
ii. The cost is {{{15000+75*500=52500}}} dollars.
iii. The profit is the revenue minus the cost, so it is {{{75000-52500=22500}}} dollars.