3205Assignment1 - Linear Programming and Integer Programming Assignment 1 October 4 2016(Submit on or before the class of Monday The first Mid-term exam

# 3205Assignment1 - Linear Programming and Integer...

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Linear Programming and Integer Programming Assignment 1 October 4, 2016 (Submit on or before the class of October 17, 2016, Monday) The first Mid-term exam will be on October 17, 2016, Monday 1. Solve the following problem by showing the simplex tableau and row operations performed in each iteration: maxx1,x2,x3Rn4x1+ 3x2+ 6x3s.t.3x1+x2+ 3x3302x1+ 2x2+ 3x340x1, x2, x30.2. Consider the following problem:maxx1,x2Rn2x1+ 3x2s.t.x1+ 2x24x1+x2= 3x1, x20.(a) Solve the above problem by graphical method. Show the feasible set, all corner-point feasible solutions,and their respective objective function values.(b) Solve the above problem by the Big M method. Show the simplex tableau and row operations performedin each iteration.3. The following is anoptimalLP tableau:zx1x2x3x4x5RHS100032z*0100-112001010600011-12for the following problemmaxxRnc0xs.t.Axbx0.wherex= (x1, x2) andx3,x4,x5in the tableau are slack variables. 1
(a) Use matrix manipulations to find A, b and c. (b) What is the optimal objective function value, i.e., z * , in the above tableau? 4. Consider the following problem4.4-6.Consider the following problem.MaximizeZ3x15x26x3,subject to2x1x2x34x12x2x34x1x22x34x1x2x33andx10,x20,x30. 2 x 1 2 3 8 and x 1 0, x 2 0, x 3 0. D,I (a) Work through the simplex method step by step in algebraic form. D,I (b) Work through the simplex method step by step in tabular form. C (c) Use a software package based on the simplex method to solve the problem.