Welte Mutual funds has just obtained $100,000 by converting industrial bonds to

Question

Welte Mutual funds has just obtained $100,000 by converting industrial bonds to cash and is now looking for other investment opportunities. Based on Welte's current investments, the firms top analyst recommends that all new investments be made in the oil industry, steel industry, or in government bonds. Specifically, the analyst has identified 5 investment opportunities and projected their annual rate of return. (Following is in a table of investments and projected rate of return in %.) Atlantic oil 7.3%, Pacific oil 10.3%, Midwest steel 6.4%, Huber steel 7.5%, and government bonds 4.5%. Some guidelines are...Neither industry (steel or oil) 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. I need to formulate a linear programming model (listing the objective function and constraints.) Can you help me with the excel portion of the problem? I don't know how to plug the numbers in.

Explanation / Answer

First define your variables and state the units of measure. I'll call them x1 through x5 to represent the number of dollars put into each of the listed investments, in order. Next construct your objective function. The return on each investment is the rate of return, times the dollars invested. The total return is then the sum of the five. In other words, "maximize .073x1 + .103x2 + .064x3 + .075x4 + .045x5". What stops you from getting infinite total return? Well, for one thing, you're limited by the $100,000 of working capital, to be split among these five investements. So "x1+x2+x3+x4+x5=100000". But there are also guidelines that must be followed. Neither industry can receive more than $50,000. So that's: x1+x2

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