Optimization Question: Day Trader wants to invest a sum of money that would gene

Question

Optimization Question:

Day Trader wants to invest a sum of money that would generate an annual yield of at lealst $10,000. Two stock groups are available: blue chips and high tech, with average annual yields of 10% and 25%, respetively. Through high-tech stocks provide higher yield, they are more risky, and Trader wants to limit the amount invested in these stocks to no more than 60% of the total investment.
What is the minimum amount Trader should invest in each stock group to accomplish the investment goal?

Explanation / Answer

Let,
X1: Dollars invested in blue chips.
X2: Dollars invested in high tech.

Min Z = X1 + X2
subject to
(1)0.1 X1 + 0.25 X2 10000
(2)X2 .6 (X1+X2) to equal = 0.6 X1 - 0.4 X2 0

Where X1 , X2 0
The optimum solution is ( 25000 , 37500 )
Then X1 = 25000,X2 = 37500, Max Z = 25000

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