In: Operations Management
Welte Mutual Funds, Inc., located in New York City has just obtained $100,000 by converting industrial bonds to cash and is now looking for other investment opportunities for these funds. Based on Welte’s current investments, the firm’s top financial analyst recommends that all new investments be made in the oil industry, steel industry, or in government bonds. Specifically, the analyst has identified five investment opportunities and projected their annual rate of return. The investments and rates of return are shown in the following table:
INESTMENT OPPORTUNTIES FOR WELTE MUTUAL FUNDS
Investment |
Projected rate of return % |
Atlantic Oil |
7.3 |
Pacific Oil |
10.3 |
Midwest Steel |
6.4 |
Huber steel |
7.5 |
Government bonds |
4.5 |
Management of Welte imposed the following investment guidelines:
Neither industry (oil or steel) should receive more than $50,000.
Government bonds should be at least 25%of the steel industry investment.
The investment in Pacific Oil, the high-return but high-risk investment cannot be more than 60% of the total oil industry investment.
Formulate a Linear-programming Model for Welte Mutual Funds. (20 points)
What portfolio recommendations __investments and amounts __should be made for the available $100,000? Provide your Excel solution along with all the reports generated through Excel. (15 point)
Write a report that explains your findings. (15 points)
Please show steps through excel how to do this!
a) Linear-programming Model is as follows:
Decision variables: Let A, P, M, H, G be the amount to be invested in Atlantic Oil, Pacific Oil, Midwest Steel, Huber Steel and Government bonds respectively
Objective: Max 0.073A + 0.103P + 0.064M + 0.075H + 0.045G
s.t.
A+P+M+H+G <= 100000 (total funds to be invested)
A+P <= 50000 (total investment in oil industry)
M+H <= 50000 (total investment in steel industry)
G >= 0.25*(M+H) (govt bonds should be atleast 25% of steel industry)
P <= 0.6*(A+P) (Pacific Oil cannot be more than 60% of the total oil industry investment)
A, P, M, H, G >= 0
Solution of the problem using LINGO follows:
Investment to be made:
A = 20000
P = 30000
M = 0
H = 40000
G = 10000
Total returns = 8000