Question

A garage band wants to hold a concert. The expected crowd is 3,000. The average expenditure on concessions is $15. Tickets sell for $10 each, and the band's profit is 80% of the gate and concession sales, minus a fixed cost of $12,000.  

Develop a general mathematical model to find their expected profit.

Select one:

a. $30,000

b. $45,000

c. $48,000

d. $75,000

Answer 1

The general mathematical model is given by,

Y = (P / 100)*(n*a + n*b) - fixed cost

Where Y = Expected profit

P = profit of band from gate and concession, here 80%

n= expected crowd

a= cost of ticket

b=expenditure on concession

The expected crowd is 3000, hence total amount of tickets sold = 3000 * 10 = 30,000 dollars

Expenditure on concessions = 15 dollars each

Hence expected expenditure on concessions

= 3000 * 15 = 45,000 dollars

Hence total cost of gate and concession sales

= 45,000 + 30,000 = 75,000

Profit = 80 % of the cost = (75,000/100) *(80)

Profit = 60,000

Hence,

Expected profit = 60,000 - 12,000

Expected profit = 48,000 dollars