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Problem 2: Consider the following linear program: 2x1 + x2 max #1,#2 ER subject to 21 x1 -2x1 x1 + + " < 1 <5 <5 X2 X2 X2 x2 > 0 (4) 1. Make a figure that illustrates the feasible set in R². 2. Provide some integers n, m ER and matrices c ER", A € Rmxn, and be Rm such that it is in standard form maxzER cx s.t. Ax=b and x > 0.

Problem 2: Consider the following linear program: 2x1 + x2 max #1,#2 ER subject to 21 x1 -2x1 x1 + + " < 1 <5 <5 X2 X2 X2 x2 > 0 (4) 1. Make a figure that illustrates the feasible set in R². 2. Provide some integers n, m ER and matrices c ER", A € Rmxn, and be Rm such that it is in standard form maxzER cx s.t. Ax=b and x > 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 2: Consider the following linear program: 2x1 + x2 max x1,x2 ER subject to X1 X1 - 2x1 X1 x2 + X2 + x2 x2 1 - 2 VI VI VI AV 1 остан 5 5 (4) 1. Make a figure that illustrates the feasible set in R². 2. Provide some integers n, m € R and matrices c E R", A € Rmxn, and b € Rm such that it is in standard form maxxER cx s.t. Ax = b and x > 0. 3. On your figure, identify each vertex x € R² and its corresponding basis (possibly more than one) B of the columns of A so that N = 0 where N = {1,...,n} \ B. 4. Solve the linear program using the simplex algorithm in tableau form. Report the iterations on your figure. 5. Use the dual simplex algorithm in order to find a solution if the constraint x₁ < 2 is added.
Transcribed Image Text:Problem 2: Consider the following linear program: 2x1 + x2 max x1,x2 ER subject to X1 X1 - 2x1 X1 x2 + X2 + x2 x2 1 - 2 VI VI VI AV 1 остан 5 5 (4) 1. Make a figure that illustrates the feasible set in R². 2. Provide some integers n, m € R and matrices c E R", A € Rmxn, and b € Rm such that it is in standard form maxxER cx s.t. Ax = b and x > 0. 3. On your figure, identify each vertex x € R² and its corresponding basis (possibly more than one) B of the columns of A so that N = 0 where N = {1,...,n} \ B. 4. Solve the linear program using the simplex algorithm in tableau form. Report the iterations on your figure. 5. Use the dual simplex algorithm in order to find a solution if the constraint x₁ < 2 is added.
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