Question

you run a school in florida. fixed monthly cost is $5,364.00 for rent and utilities, $6,116.00 is spent in salaries and $1,108.00 in insurance. also every student adds up to $104.00 per month in stationary, food etc. you charge $635.00 per month from every student now. you are considering moving the school to another neighborhood where the rent and utilities will increase to $10,787.00, salaries to $6,578.00 and insurance to $2,118.00 per month. variable cost per student will increase up to $179.00 per month. however you can charge $1,184.00 per student. at what point will you be indifferent between your current mode of operation and the new option?

Answer 1

To be indifferent between the current mode of operation and the new option, you need to compare the costs and revenues for each option. The new option would be more profitable for any number of students greater than 0.

Step-by-step explanation:

To determine at what point you would be indifferent between your current mode of operation and the new option, you need to compare the costs and revenues for each option.

For the current mode of operation, the total fixed costs are $5,364 + $6,116 + $1,108 = $12,588 per month. The variable costs per student are $104. The revenue per student is $635. Therefore, the monthly profit per student is $635 - $104 = $531.

For the new option, the total fixed costs are $10,787 + $6,578 + $2,118 = $19,483 per month. The variable costs per student are $179. The revenue per student is $1,184. Therefore, the monthly profit per student is $1,184 - $179 = $1,005.

To be indifferent between the two options, the profit per student in each must be equal. Therefore, you need to find how many students would make $531 per student equal to $1,005 per student. Let's call this number of students 'x'.

531x = 1,005x

Subtracting 531x from both sides gives us 1,005x - 531x = 0

Combining like terms, we have 474x = 0

Dividing both sides by 474 gives us x = 0

Therefore, you would be indifferent between your current mode of operation and the new option when the number of students is 0. This means that the new option would be more profitable for any number of students greater than 0.