An automobile company is sponsoring a charity golf tournament to raise money for

Question

An automobile company is sponsoring a charity golf tournament to raise money for a charity. There are two possible venues: RTJ Golf Resort, which charges a fixed rental cost of $7,380 plus an additional fee of $90 per person. The automobile company will charge $350 per ticket if the event is at RTJ Golf Resort. Wynlakes Golf & Country Club, which charges a fixed rental cost of $2,000 plus $140 per person. The automobile company will charge $323 per ticket if the event is at Wynlakes. The automobile company will also have $1,700 in costs for administration, marketing, and entertainment at both venues. What is the fewest number of tickets to be sold for the company to be indifferent between the two venues? (Your answer can be a decimal number.)

Explanation / Answer

In order to be indifferent, the profit has to be equal for both venues.

Profit = Number of tickets x (Price - Unit variable cost) - Fixed costs

Let indifference quantity of tickets be Q.

For RTJ,

Profit ($) = Q x (350 - 90) - 7,380 - 1,700 = 260Q - 5,680

For Wynlakes,

Profit ($) = Q x (323 - 140) - 2,000 - 1,700 = 183Q - 3,700

For equivalence,

260Q - 5,680 = 183Q - 3,700

77Q = 1,980

Q = 25.71

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