The Heinlein and Krampf Brokerage firm has just been instructed by one of its cl

Question

The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:
(a) Municipal bonds should constitute at least 20%
of the investment.
(b) At least 40% of the funds should be placed in a
combination of electronic firms, aerospace firms,
and drug manufacturers.
(c) No more than 50% of the amount invested in
municipal bonds should be placed in a high-risk,
high-yield nursing home stock.
Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines prepare a list of high-quality stocks and bonds and their corresponding rates of return.

I am trying to solve this using Excel Solver and running into issues. What would my constraints be in the Excel formula? I know all the investments must be less than $250,000.

Explanation / Answer

Let "a" be the variable for bonds and "b" be the variable for stocks. Let c be the variable for the combination of  electronic firms, aerospace firms, and drug manufacturers. Let d be the variable for high-risk, high-yield nursing home stock.

Now, the returns from bonds or stocks are not given. Assuming the returns to be "x" and "y"% respectively, the totao returns will be x%*a+y%*b. This is our objective function and has to be maximized.

Constraints are:

(i) a+b<=250,000 (the total amount to be invested cannot be more than 250,000)

(ii) a>=50,000 (municipal bonds should be atleast 20% of investment = 20% of 250,000 = 50,000)

(iii) 0.40*(a+b) (at least 40% of the funds should be placed in a combination of electronic firms, aerospace firms,
and drug manufacturers.)

(iv) c+d = a+b (assuming the portfolio is consisting of a combination of  electronic firms, aerospace firms, and drug manufacturers and high-yield nursing home stock)

(v) 0.50b<=d (No more than 50% of the amount invested in municipal bonds should be placed in a high-risk,
high-yield nursing home stock).

(vi) a,b>=0 (it cannot be negative)

The solver cannot be used to find a solution as the return from each class is not given and hence the expected return to be maximized cannot be formulated in excel.

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