Beball camp example covered in the class, let's assume the segment size is 9000, price per participant is $90, frequency is 1, variable cost per person is $5, TFC = $9,000. Based on the assumption provided above, what percentage of the segment should participate if the program wants to make $1500 profit? Group of answer choices about 1.78% about 1.14% about 1.92% about 1.37%

The correct answer is D. About 1.37%

Explanation:

1. Let's review the information given to us to answer the question correctly:

Segment size = 9,000

Number of participants in the camp = x

Total Fixed Cost (TFC) = $ 9,000  

Variable Cost per Person = $ 5  

Price per Person = $ 90

Profit = $ 1,500

2. Based on the assumption provided above, what percentage of the segment should participate if the program wants to make $1500 profit?

We can calculate the variable cost, this way:

Total Variable Cost = Variable cost per person * Number of participants

Total Variable Cost = $ 5 * x

Total Variable Cost = $ 5x

We can calculate the total cost of the program, this way:

Total Cost of the program = Total Variable cost + Total Fixed Cost  

Total Cost of the program = $ 5x+ $ 9,000

Total cost of the program = $ 9,000 + 5x

We can calculate the revenue of the program, this way:

Total revenue of the program = Price per person * Number of participants + Profit

Total revenue of the program = $ 90 * x + $ 1,500

Total revenue of the program = $ 90x + $ 1,500

For Break-even:

Total Variable cost + Total Fixed Cost = Price per person * Number of participants

Replacing with the values we know and solving for x:

9,000 + 5x =  90x

5x - 90x = - 9,000  (Like terms)

-85x = -9,000

x =  -9,000/-85

x = 106 (rounding to the next whole)

For $ 1,500 of profits:

Number of participants at break-even + Profits/Price per participant

106 + 1,500/90 = 106 + 16.7 = 123

123/1,500 = 0.0137 = 1.37% (Rounding to two decimal places)

The correct answer is D. About 1.37%

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