Question

You run a school in Florida. Fixed monthly cost is $6000 for rent and utilities, $5000 is spent in salaries and $1000 in insurance. Also every student adds up to $90 per month in stationary, food etc. You charge $700 per month from every student now. You are considering moving the school to another neighborhood where the rent and utilities will increase to $10000, salaries to $6000 and insurance to $2000 per month. Variable cost per student will increase up to $150 per month. However, you can charge $1000 per student. At what point will you be indifferent between your current mode of operation and the new option?

1) 30
2) 20
3) 25
4) 40

Answer 1

To determine the point of indifference between the current mode of operation and the new option for the school, we compare the total costs and revenues for both scenarios. Using this comparison, the school will be indifferent when it has 20 students.

Step-by-step explanation:

To determine at what point the school will be indifferent between its current mode of operation and the new option, we need to compare the total costs and total revenues for both scenarios.

Current mode of operation: The total cost per student is the sum of fixed costs and variable costs, which is ($6,000 + $5,000 + $1,000) + ($90) = $12,090 per student per month. The total revenue per student is $700 per month.
New option: The total cost per student is the sum of fixed costs and variable costs, which is ($10,000 + $6,000 + $2,000) + ($150) = $18,150 per student per month. The total revenue per student is $1,000 per month.

To find the point of indifference, we set the total costs equal to the total revenues:
$12,090 = $700x
$18,150 = $1,000x

Solving for x gives:
x ≈ 17.2717 (approximately)

Since the number of students cannot be fractional, the school will be indifferent between its current mode of operation and the new option when it has 17 or 18 students. Therefore, the correct answer is 2) 20.