4390 Operations Management all 2017 1. [Model Formulation of Linear Programming
ID: 365860 • Letter: 4
Question
4390 Operations Management all 2017 1. [Model Formulation of Linear Programming - Finance) Eastern Alabama Trust invests in various types of securities. They have $6 million for immediate investment and wish to maximize the interest cameaed earned over the Risk is not a factor. Four investment alternatives include Bonds, Stocks, and Land. The expected return for Bonds is 9%, Stocks 12%, and Land 7%·The maxim $3 million for Bonds, $3 million for Stocks, and $1 million for Land. has specified at least 30% of the investment has to be in corporate bonds 10% of the investment is to be in Land. The objective um amount to be invested for each alternative is To structure the portfolio, the Senior VP and common stock; and no more than is to maximize the return. Formulate a linear model. (a) What are the Decision Variables? (b) What is the Objective Function? (c) What are Constraint Equations including non-negativity constraints?Explanation / Answer
Decision Variables:
S
Amount of investment to be invested in stocks
B
Amount of investment to be invested in bonds
L
Amount of investment to be invested in Land
Objective Function:
Expected returns on bonds is 9%, Stocks 12% and Land 7%. The return function for investment is given as follows:
Max Z = 0.9B + 0.12S + 0.7L
Subject to:
Total amount to be invested
B + S + L <= 6
Maximum amount to be invested in bond
B <= 3
Maximum amount to be invested in Stocks is $3M
S <= 3
Maximum amount to be invested in Land is $1M
L <= 3
At least 30% of the investment has to be in corporate bonds and stock
B + S >= 0.3(B + S + L)
0.7B + 0.7S – 0.3L >= 0
No more than 10% of the investment is to be done in Land
L <= 0.1(B + S + L)
-0.1B – 0.1S + 0.9L <= 0
Non-negative constraint
B, S, L >= 0
S
Amount of investment to be invested in stocks
B
Amount of investment to be invested in bonds
L
Amount of investment to be invested in Land
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