Millbridge Township provides a variety of summer recreation alternatives. You can belong to the town pool, play tennis, or play golf. Summer passes allowing residents to use these facilities are sold each year. Twenty-five percent of the season's passes that are purchased are golf passes, 35 percent are for tennis, and the rest are for the pool. The golf passes are $30, the tennis passes are $50, and the pool passes are $70. The cost of providing these services is mostly fixed, with a $3 variable cost per pass, regardless of type. The fixed cost of operating the summer recreation program is $250,000.

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How many people must buy recreation passes for the town to break even?

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raphealnwobi raphealnwobi · Answer 1 · 2022-03-21T11:36:36+01:00

5000 people must buy recreation passes for the town to break even.

Break even is the point at which the profit made is 0, that is the cost of production is equal to the revenue.

Let x represent the total number of people, hence:

Total cost = 250000 + 3x

Number of golf pass = 25% of x = 0.25x

Number of tennis pass = 35% of x = 0.35x

Number of pool pass = (100% - 35% - 25%) of x = 0.4x

Total revenue = ($30 * 0.25x) + ($50 * 0.35x) + ($70 * 0.4x) = 53x

At breakeven:

Total cost = total revenue

53x = 250000 + 3x

x = 5000

5000 people must buy recreation passes for the town to break even.

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