To find the point of indifference between the current operation and the new option, we need to calculate the total cost and revenue for both scenarios and set them equal to each other.
Current Operation:
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Fixed Costs:
- Rent and utilities: $5,238.00
- Salaries: $6,113.00
- Insurance: $1,219.00
Total Fixed Costs = \( 5,238 + 6,113 + 1,219 = 12,570 \)
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Variable Costs per Student: $105.00
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Revenue per Student: $602.00
Let \( n \) be the number of students.
- Total Revenue = \( n \times 602 \)
- Total Variable Costs = \( n \times 105 \)
Total Cost = Total Fixed Costs + Total Variable Costs = \( 12,570 + 105n \)
New Operation:
-
Fixed Costs:
- Rent and utilities: $10,593.00
- Salaries: $6,493.00
- Insurance: $2,327.00
Total Fixed Costs = \( 10,593 + 6,493 + 2,327 = 19,413 \)
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Variable Costs per Student: $153.00
-
Revenue per Student: $1,114.00
- Total Revenue = \( n \times 1,114 \)
- Total Variable Costs = \( n \times 153 \)
Total Cost = Total Fixed Costs + Total Variable Costs = \( 19,413 + 153n \)
Set the total revenue equal to total costs for indifference:
\[ 12,570 + 105n = 19,413 + 153n \]
Rearranging the equation:
\[ 12,570 - 19,413 = 153n - 105n \]
\[ -6,843 = 48n \]
\[ n = \frac{-6,843}{48} \]
\[ n = -142.56 \]
Since the number of students cannot be negative, this means that under the current costs and revenues of both scenarios, operating costs of the new option are always higher than the current one. Therefore, you’ll never be indifferent between the two options regardless of how many students you have; the new option is not financially viable compared to the current operation.
Thus, there is no point of indifference in this case.