Question

You run a school in Florida. Fixed monthly cost is $5,021.00 for rent and utilities, $5,703.00 is spent in salaries and $1,741.00 in insurance. Also every student adds up to $101.00 per month in stationary, food etc. You charge $619.00 per month from every student now. You are considering moving the school to another neighborhood where the rent and utilities will increase to $11,633.00, salaries to $6,560.00 and insurance to $2,034.00 per month. Variable cost per student will increase up to $190.00 per month. However you can charge $1,122.00 per student. At what point will you be indifferent between your current mode of operation and the new option?

Answer 1

Suppose there are ‘x’ no. of students. So, the total profit from each operation will be:

Profit From Operation 1 = 619x – 5,021 – 5,703 – 1,741 – 101x.

                                                = 518x – 12,465.                                                                                …..(1)

Profit From Operation 2 = 1,122x – 11,633 – 6,560 – 2,034 – 190x.

                                                = 932x – 20,227.                                                                                …..(2)

Equating (1) and (2) we get:

518x – 12,465 = 932x – 20,227.

414x = 7,762

X=18.74

X= 19 ( approx).

Thus, when there would be 19 students than we would be indifferent between the operations.