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Homework 9

# Homework 9 - Math 171A Mathematical Programming Instructor...

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Math 171A: Mathematical Programming Instructor: Philip E. Gill Winter Quarter 2009 Homework Assignment #9 Due Friday March 13, 2009 The final will be held Wednesday, March 18 at 3pm. Starred exercises require the use of Matlab . Exercise 9.1. * For the following linear program, construct an equivalent standard-form problem in which the objective function is minimized and the constraints have the form Ax = b , x 0. Starting at the vertex where all slack variables are basic, solve the problem using the standard-form simplex method (Algorithm 5.1 in the Class Text). At every iteration, record (i) the values of the basic variables; (ii) the indices of the basic and nonbasic variables; (iii) the multiplier π and the reduced cost vector z N ; (iv) the search direction p B ; and (v) the step to the nearest constraint. maximize - 10 x 1 + 32 x 2 + 48 x 3 + 54 x 4 subject to 2 x 1 + 3 x 2 + 5 x 3 + x 4 24 5 x 1 + 2 x 2 + x 3 + 3 x 4 32 8 x 1 + 5 x 2 + 6 x 3 + 10 x 4 64 3 x 1 + 6 x 2 + 9 x 3 + 12 x 4 81 x 1 , x 2 , x 3 , x 4 0 .

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