Hello, need help with the Optimization Modeling homework, Thanks.

Problem #1

The College of Business Tech is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, course development, and staff recruitment and development is $360,000. The college plans to charge tuition of $18,000 per student per year. However, the university administration will charge the college $12,000 per student for the students enrolled each year for administrative costs and its share of the tuition payments.

(a) How many students does the college need to enroll in the first year

to break even?

(b) The enrollment capacity for this program is 100 students. If the

college can enroll 100 students the first year, how much profit

will it make?

(c) The college believes it can increase tuition to $24,000. Find

the new break-even point assuming the other costs remain the same.

(d)If the college can only enroll 35 students under this new tuition

plan; use your answer in (c) to indicate whether they would be

losing or making money?

(10) Problem #2

A plant is operating at its normal capacity of 50,000 units per year. The annual fixed costs are $20,000 and the variable cost is $0.12 per unit.

a. What must be the minimum unit selling price if a loss situation is to be prevented?

b. If the demand increases to 70,000 units per year, the plant can operate on an overtime

basis at an additional cost of $0.03 per unit (total cost = $.15 per unit)for only those

additional items. Assuming the selling price calculated in part (a), what would be the

annual profit?

(30) Problem #3

Given the following production cost table

Production Fixed Variable Total Marginal Marginal

Output Q Cost Cost Cost Revenue Profit Cost Revenue

(A) (B) (C) (D) (E) (F) (G) (H)

1 $300 $100 $125

2 $300 $180 $250

3 $300 $240 $375

4 $300 $290 $500

5 $300 $345 $625

6 $300 $415 $745

7 $300 $505 $860

8 $300 $620 $970

9 $300 $765 $1065

10 $300 $945 $1135

a. Calculate the total cost and profit for each production quantity.

b. Plot total cost and income against production quantity

c. From the plot in (b), determine the break-even point(s).

d. Plot profit against production quantity.

e. Compute marginal cost and marginal revenue for each production quantity and

plot these against production quantity on the same graph.

You may use EXCEL for doing this problem.