Question

Max Welte has converted an industrial bond to cash and is now considering other investment opportunities for the $100,000 in his cash account. As his financial advisor, you have recommended that all new investments be made in the oil industry, in the steel industry, on in government bonds. Specifically, you have identified five investment opportunities and their projected annual rates of return. The investments and rates of return are shown in this table:

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

Max is a fairly knowledgeable investor and wants to be sure his portfolio is diversified. He has imposed the following guidelines:

a) Neither industry (oil or steel) should receive more than $50,000.

b) Government bond should be at least 25% of the steel industry investments.

c) The investment in Pacific Oil, a high-return but high-risk investment, cannot be more than 60% of the total oil industry investment.

Formulate this investment problem as a linear programing (LP) problem. You are not required to solve the problem.

Answer 1