the college of business is planning to begin an online MBA program. the initial

Question

the college of business is planning to begin an online MBA program. the initial start-up cost for computing equipment, facilities, course and development is $ 400,000. the college plans to charge tuition of $20,000 per student per year. However, the university administration will charge the college $12,000 per student enrolled each year for administrative costs and its share of the tuition payments

a) Determine the costs, revenue, and profit functions in terms of the number of students enrolled.
b)how many students would the college need to enroll in the first year if they would like to make a profit of at least 5% of revenue?
c) the college believes it can increase tuition from $20,000 to $24,000 per year. however, doing this will reduce enrollment from 65 to 40 students. should the college consider doing this?

Explanation / Answer

Let p(x), r(x), and c(x) be the profit, revenue, and profit functions. Let x = number of students enrolled. There are two types of costs: fixed and variable costs. The fixed cost here is the $400,000. The variable cost depends on the number of students enrolled. Since the college is being charged $12,000 per student we represent this in our equation as 12000x. Thus, c(x) = 12000x + 400000. The revenue is tuition payments so 20000x. Thus, r(x) = 20000x. Profit = revenue - costs. Thus, p(x) = 20000x - (12000x + 400000) = 8000x - 400000

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