Final answer:
To break even, the college needs to enroll approximately 59 students in the first year, and if it can enroll 75 students, it would make a profit of $450,000.
Step-by-step explanation:
To break even, the college needs to cover its initial start-up cost of $350,000. This cost includes computing equipment, facilities, course development, and staff recruitment and development. The university administration will charge the college $12,000 per student for the first 100 students enrolled each year, so we'll subtract this administrative cost from the tuition fee of $18,000 per student per year to determine the profit per student. By dividing the total start-up cost by the profit per student, we can calculate the number of students needed to break even.
The profit per student is calculated by subtracting the administrative cost of $12,000 from the tuition fee of $18,000:
Profit per student = Tuition fee - Administrative cost = $18,000 - $12,000 = $6,000
To find the number of students needed to break even, we divide the total start-up cost of $350,000 by the profit per student of $6,000:
Number of students needed = Total start-up cost / Profit per student = $350,000 / $6,000 = 58.33
Therefore, the college needs to enroll approximately 59 students in the first year to break even.
If the college can enroll 75 students in the first year, we can calculate the profit by multiplying the profit per student of $6,000 by the number of students:
Profit = Profit per student x Number of students = $6,000 x 75 = $450,000
Therefore, the college would make a profit of $450,000 if it can enroll 75 students in the first year.