Linear Programming. Concert Contract

Question

You are a concert promoter and sign a contract with Keith Urban. In the contract, you guarantee the attendance of at least 12,500 and total ticket receipts of at least $225,000. The tickets to the concert cost $15 and $25, and you agree to give Keith Urban $5 out of the $15 tickets and $7.50 out of each $25. If the stadium can safely handle at most 20,000 fans, then what is the minimum amount of money you have to guarantee Keith?

Find the variables, the constraints, the cost equation and solve to graph

Answer 1

Variables:

x = Number of $15 tickets sold

y = Number of $25 tickets sold

Constraints:

You guarantee the attendance of at least 12,500: x + y ≥ 12,500

The stadium can safely handle at most 20,000 fans: x + y ≤ 20,000

You guarantee total ticket receipts of at least $225,000: 15x + 25y ≥ 225,000

You can also assume x ≥ 0 and y ≥ 0 (can't have negative ticket sales)

Cost Equation:

You agree to give Keith Urban $5 out of the $15 tickets and $7.50 out of each $25: Cost = 5x + 7.5y

Can you complete it from here? Remember, you're trying to find the minimum cost, not the maximum.