Question

A local arena is negotiating a contract with a tourist ice skating show, icey blades. Icey blades charge a flat fee for $60000 per night plus 40 percent of the gate receipts. The civic arena plans to charge one price of all seats $1.250 per ticket. A) Determine the number of tickets which must be sold each night in order to break even? B) what would nightly profit equal if average attendance in 7500 per night?

Answer 1

To break even the local arena must sell approximately 70,589 tickets. They would have a loss of $47625.

Explanation:

The cost per night of the Icey blades contract can be expressed as a function of the gate receipts, with the flat cost added by 40% of all the gate receipts sold. This expression is shown below:

`cost(x) = 60000 +0.4*x`

Since each ticket costs $1.25, then the revenue of the arena can be shown as:

`revenue(x) = 1.25*x`

In order to break even the revenue must be equal to the cost, so:

`revenue(x) = cost(x)\\1.25*x = 60000 + 0.4*x\\1.25*x - 0.4*x = 60000\\0.85*x = 60000\\x = (60000)/(0.85) = 70,588.24`

To break even the local arena must sell approximately 70,589 tickets.

If the average attendance was 7500 per night, the profit would be:

`profit = revenue(7500) - cost(7500)\\profit = 1.25*7500 - 60000 + 0.4*7500\\profit = 9375 - 60000 + 3000\\profit = -47625`

They would have a loss of $47625