Wednesday Feb. 27, 2013
TIME ALLOWED 75 min.
Please read the questions carefully!
Show your methodology, final answers carry near zero points. There are 6 pages including the cover page in this exam. Please make sure all pages are attached. TURN YOUR CELL PHONE OFF!!
Student Name: ___________________________________________ Student number: ____________________________
Question| Maximum mark| Student mark|
1| 11| |
2| 10| |
3| 12| |
4| 17| |
TOTAL| 50| |
Question 1: (11 marks)
The law firm of Smith, Jones, and Greene provides accounting service for some of its clients. The person who handles this service and her secretary cost the law firm an average of $80,000 per year in salary and benefits. Furthermore, the law firm incurs an additional charge of $50 per client for computer time, postage, and supplies. Clients are charged $300 a year for these accounting services. a) Determine the cost, revenue, and profit functions for the law firm in terms of the number of clients. You can use “x” to denote the number of clients. (3) C(x) = 80,000 + 50x
R(x) = 300x
P(x) = -80,000 + 250x
b) What profit/loss would the firm realize if 354 clients use its accounting service each year? (2) P(x) = -80,000 + 250x
P(x = 354) = -80,000 + 250(354)
P(x = 354) = -8,500 (a loss of $8,500)
c) A local accounting firm has offered to provide comparable service to the law firm for a fee of $600 per client. The law firm needs to decide whether to offer the accounting service to its clients in-house or outsource them to the accounting firm. Assuming 300 clients per year, would the law firm be better off using its own staff, or using the outside accounting firm? (3) Cost incurred if accounting service provided in in-house:
C(x = 300) = 80,000 + 50(300) = $95,000
Cost incurred if accounting service provided outside accounting firm: C(x = 300) = 600(300) = $180,000
Better to use in-house for the cost incurred would be less
d) At what level of client usage would the two alternatives produce the same profit or loss? (3)
We need to set the cost of the two options equal to one another; since the revenues to the law firm will be the same regardless of the method selected.
80,000 + 50x = 600x
-550x = -80,000
X = 145.45 clients
Question 2: (10 marks)
A financial adviser recently received a call from a client who wanted to invest a portion of his $150,000 inheritance for a year. The client would like to invest some of his inheritance but also like to use some of the money to take a vacation. After discussing the matter, the client and the adviser agreed that a mutual fund, corporate bonds, and a money market account would make suitable investments. The client was willing to leave allocation of the funds among these investment vehicles to the financial adviser, but with these provisions: - The amount invested in the money market account should be between 20% and 30% of the total investment. - The investment must produce at least $12,000 annually in interest. - To keep risk levels low, investment in corporate bonds must be at most as much as the amount invested in mutual funds. The client would like to minimize the amount he invests so that he can use the remainder of the money for his vacation. The annual return would be 11% for the mutual funds, 8% for the bonds, and 7% for money markets. Keep in mind the entire inheritance does not need to be invested; in fact the client wants to invest the least amount. Formulate a linear programming model for this problem. DO NOT SOLVE.
Decision variables: (2)
Let M be the dollar amount invested in mutual funds.
Let B be the dollar amount invested in corporate bonds.
Let N be the dollar amount invested in money market.
Maximize total investment:Z = M + B + N