CCE 6100 HW2 edited

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Western Michigan University *

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6100

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Civil Engineering

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Feb 20, 2024

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pdf

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WESTERN MICHIGAN UNIVERSITY CCE-6100-100 - Civil Systems Analysis HW.2 Done by: Aws Tarawneh
1. Solve the following linear program using the graphical solution procedure: Feasible area Max at 100,50 (100*5+50*5)=750
2. Given the linear program 2.1. Write the problem in standard form Max 3A+4B+0S1+0S2+0S3 S.t -1A+2B+0S1 =8 1A+2B + 0S2 =12 2A+1B + 0S3=16 A, B, S1, S2, S3≥0 2.2. Solve the problem using the graphical solution procedure Intersection 1 Intersection 2 Feasible area
At Intersection 1 -1A+2B=8 1A+2B=12 B=5 A=2 3A+4 B=3*2+4*5=26 At Intersection 2 1A+2B=12 2A+1B=16 A=6.6667 B=2.6667 3A+4 B=30.66 Lingo output Global optimal solution found. Objective value: 30.66667 Infeasibilities: 0.000000 Total solver iterations: 2 Model Class: LP Total variables: 2 Nonlinear variables: 0 Integer variables: 0 Total constraints: 6 Nonlinear constraints: 0 Total nonzeros: 10 Nonlinear nonzeros: 0 Variable Value Reduced Cost A 6.666667 0.000000 B 2.666667 0.000000 Row Slack or Surplus Dual Price 1 30.66667 1.000000 2 9.333333 0.000000 3 0.000000 1.666667 4 0.000000 0.6666667 5 6.666667 0.000000 6 2.666667 0.000000
2.3.What are the values of the three slack variables at the optimal solution? A= 20/3 B=8/3 S1=8+A-2B= 8+ (20/3)-2(8/3) = 28/3 S2=12-A-2B=12-(20/3)-2(8/3) = 0 S3=16-2A-B=16-2(20/3) -(8/3) =0 3. 3.1.What is the recommended investment portfolio for this client? What is the annual return for the portfolio? Max. 0.12 I + 0.09B S.t. I+B ≤ 50,000 maximum to invest I ≤ 35,000 max investment in the Internet fund. 6I+4B≤240 max risk rating I, B≥ 0 I= Internet Fund Investment. B= Blue clip Fund Investment. Using Lingo Global optimal solution found. Objective value: 5.100000 Infeasibilities: 0.000000 Total solver iterations: 2 Model Class: LP Total variables: 2 Nonlinear variables: 0 Integer variables: 0 Total constraints: 6 Nonlinear constraints: 0 Total nonzeros: 9 Nonlinear nonzeros: 0 Variable Value Reduced Cost I 20.00000 0.000000 B 30.00000 0.000000 Row Slack or Surplus Dual Price 1 5.100000 1.000000 2 0.000000 0.3000000E-01 3 15.00000 0.000000 4 0.000000 0.1500000E-01
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