SOLUTION: Mr. Moody has decided to invest at most N$100 000 in securities in the form of corporate stocks. He has classified his options into three groups of stocks: blue-chip stocks that he

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Question 1148052: Mr. Moody has decided to invest at most N$100 000 in securities in the form of corporate stocks. He has classified his options into three groups of stocks: blue-chip stocks that he assumes will yield a 10% return on his investment within a year, growth stocks that he assumes will yield a 15% return on his investment within a year, and speculative stocks that he assumes will yield 20% return on his investment within a year. Because of the relative risks involved in his investment, he has further decided that no more than 30% of his investment should be in growth and speculative stocks and at least 50% of his investment should be in blue chip and speculative stocks. Determine how much Mr. Moody should invest in each class of stocks in the hope of maximizing the return on his investments.
Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
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Let X = investment into Blue-ship   stocks (yield 10% return);

    Y = investment into growth      stocks (yield 15% return);

    Z = investment into speculative stocks (yield 20% return).


Then the objective function to MAXIMIZE is the total return 

    P(X,Y,Z) = 0.1X + 0.15Y + 0.2Z    (1)


The constraints are

    X + Y + Z <= 100000,          (2)    ("decided to invest at most N$100 000")

    Y + Z <= 0.3*(X + Y + Z)      (3)    ("no more than 30% of his investment should be in growth and speculative stocks")

    X + Z >= 0.5*(X + Y + Z)      (4)    ("at least 50% of his investment should be in blue chip and speculative stocks.")

    X >= 0,  Y >= 0,  Z >= 0.     (5)


The constraints  (3) and (4)  can be reduced to the standard form

    0.3X -0.7Y - 0.7Z >= 0        (3')  

    0.5X - 0.5Y + 0.5Z <= 0       (4')   


So, the set up is this set of equalities and inequalities  (1), (2), (3'), (4') and (5).


With this setup, find an appropriate solver and use it to get the numerical answer.