12 An investment manager is considering stocks X1, X2, and X3 for investment. Market research shows the following inform

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12
An investment manager is considering stocks X1, X2, and X3 for
investment. Market research shows the following information (per
stock)
X1
X2
X3
cost $100
risk measure 8
price annual growth rate: 9%
annual return: $14
cost $120
risk measure 10
price annual growth rate: 13%
annual return: $15
cost $80
risk measure 7
price annual growth rate: 8%
annual return: $20
Based on his experience, the manager has set the following
priorities for the investment:
(1) The total amount invested should be at least $90,000.
(d1)
(2) The minimum annual average growth rate in stock prices is
12%. (d2)
(3) The risk factor of all stocks should not exceed an average
of 5. (d3)
(4) The total annual return should be $15,000. (d4)
The constraint for the amount of investment can be written
as:
100X1 + 120X2 + 80X3 + d1- - d1+ ≤ 90,000
100X1 + 120X2 + 80X3 + d1- - d1+ = 90,000
100X1 + 120X2 + 80X3 + d1- - d1+ = 80,000
100X1 + 120X2 + 80X3 ≥ 90,000
100X1 + 120X2 + 80X3 + d1- - d1+ ≥ 80,000