Assume you are an analyst with an online university say UOP

Assume you are an analyst with an online university say UOP. The Admissions Director (AD) wants to determine the optimum number of students for each ECO561 class. You are provided with the following data: Tuition is $1250 per student. Instructor Pay $2500 Other incidental (variable) costs - $1000.00 Variable cost increases by 10% per each additional student How many students will you recommend to the AD? What would be the profit for the given number of students? Is this a profit maximizing number oif students? Now assume that variable cost increases by 15% for each additional student, what is the new prrofit maximizing number of students? What is the relevance of the marginal rule (MR = MC) in your decision making?

Solution

Change in Revenue per additional student = $1250

addtional cost per additional student = 10%*1000=$100

MR =MC

1250=100*x

x=12.5 . Thus each class should have 12.5 students

Total Revenue= 1250*12.5=15625

Total cost = 2500+1000=3500

Profit=15625-3500= $12125

If VC increase to 15% for each additional student , additional cost for each additional student= 15%*1000=$150

1250=150*x

x=8.3 (profit maximizing number of students )

Total revenue= 1250*8.3=10375

Total cost = 3500

Profit = 10375-3500=6875.

The problem is solved under the assumption that the analyst will follow MR=MC in determining the number of students