Math For Business

A man has decided to invest at most $90,000 in securities in the form of corporate stocks. He has three options: blue chip stocks he assumes will yield a 6% return, growth stocks @ 12%, and speculative stocks @ 20%. No more than 25% of his investment should be in growth and speculative stocks and at least 15,000 of his investments should be in growth stocks. How much should he invest in each group in hope of maximizing return?

I just need to know how to set up the constraints and objective function. This is a case and a big part of my grade! THANKS!!

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  1. You have:
    Max (.06*B + .12*G + .20*S) subject to:
    B+G+S = 90,000
    G+S <= 22,500
    G >= 15,000

    You could set this up as a linear programming problem. However, getting to the optimal solution is obvious.
    G=15,000, S=7500, B=the remainder

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