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PORTFOLIO SELECTION

Welte Mutual Funds Inc., located in New York has 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. The analyst has specifically identified five investment opportunities and projected their annual rates of return. The management of Welte has imposed the following investment guidelines: 1. Neither industry should receive more than $50,000 2. Government bonds should be at least 25% of the steel industry investment 3. The investment in Pacific Oil, the high return but high risk investments, cannot be more than 60% of the total oil industry investment Investment opportunities 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

Q: What portfolio recommendations-investments and amounts –should be made for the available $100,000?

OBJECTIVE To maximise the total return for the portfolio using the projected rates given in the table FORMULATION & TECHNIQUES USED We can use the Linear Programming (LPP) model to solve the given case. Decision Variables The Decision variables used are Let, X1- Amount invested in Atlantic Oil X2- Amount invested in Pacific Oil X3- Amount invested in Midwest Steel X4- Amount invested in Huber Steel X5- Amount invested in Government bonds

The Objective Function Z = 0.073X1+0.103X2+0.064X3+0.075X4+0.045X5 The Constraints 1. X1+X2+X3+X4+X5 = 100,000 Constraint specifies available investment is $100,000 2. X1+X2