Chapter5 - Investment Science Chapter 5 Solutions to...

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Investment Science Chapter 5 Solutions to Suggested Problems Dr. James A. Tzitzouris <[email protected]> 5.1 Project Benefit-Cost Ratio 1 2 2 5/3 3 3/2 4 4/3 5 5/3 So, the approximate method based on cost-benefit ratios implies projects 1, 2, and 5 would be recommended. The optimal set of projects is the same. Note: projects 1,2, and 3 provide the same total net present value and use the entire budget. 5.2 The zero-one problem is the same as in Example 5.2 with the one additional constraint. This additional constraint can be expressed in several different ways. Here are two examples: ( x 2 + x 4 )(1 - ( x 6 + x 7 )) = 0 x 2 + x 4 x 6 + x 7 The optimal solution funds projects 4, 6, and 10 for a total cost of $4 , 700 , 000 and a total benefit of $7 , 800 , 000. 1
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5.3 The problem is to maximize 150 x 1 + 200 x 2 + 100 x 3 + 100 x 4 + 120 x 5 + 150 x 6 + 240 x 7 , subject to 90 x 1 + 80 x 2 + 50 x 3 + 20 x 4 + 40 x 5 + 80 x 6 + 80 x 7 + y 250, 58 x 1 + 80 x 2 + 100 x 3 + 64 x 4 + 50 x 5 + 20 x 6 + 100 x 7 - 1 . 1 y 250, x i ∈ { 0 , 1 } , i, y 0 .
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