381Hw4 - explicit and implicit constraints. (a) Toll booth...

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HOMEWORK 4 (1) Put the following LPs in standard form: (a) minimize x 1 - 12 x 2 - 2 x 3 subject to 5 x 1 - x 2 - 2 x 3 = 10 2 x 1 + x 2 - 20 x 3 ≥ - 30 x 2 0 , 1 x 3 4 (b) maximize 4 x 1 - 2 x 2 + x 3 subject to - x 1 + 3 x 2 - x 3 ≥ - 1 5 x 2 + 3 x 3 = 5 x 1 + x 2 + x 3 1 - 1 x 2 , - 2 x 3 2 (2) Solve the following problems using the Simplex algorithm. Show your work. Give the optimal value and the solution. (a) maximize 4 x 1 + 3 x 2 + 2 x 3 subject to x 1 + x 3 2 - x 1 - x 2 + x 1 1 x 1 + x 2 + x 3 3 0 x 1 ,x 2 ,x 3 (b) maximize 4 x 1 + 2 x 2 + 2 x 3 subject to x 1 + 3 x 2 - 2 x 3 3 4 x 1 + 2 x 2 4 x 1 + x 2 + x 3 2 0 x 1 ,x 2 ,x 3 (3) Model the following as LPs, and then solve using the lpSolve package. For each model, be sure to carefully write down your decision variables, objective,
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Unformatted text preview: explicit and implicit constraints. (a) Toll booth scheduling problem: http://www.math.washington.edu/~burke/crs/407/models/m3.html (b) Product manufacturing problem: http://www.math.washington.edu/~burke/crs/407/models/m1.html (4) Bonus: Model the following, and solve using lpSolve . Partial bonus given for modeling only. Electronics company: http://www.math.washington.edu/~burke/crs/407/models/m7.html 1...
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