First 3 parts are solved. 5-28 Consider the linear program max x1 + x2 s.t. x1 + x2 ≤ 9 -2x1 + x2 ≤ 0 x1 - 2x2 ≤ 0 x1, x2 ≥ 0 (a) Solve the problem graphically. (b) Add slacks x3,c, x5 to place the model in standard form. (c) Apply rudimentary simplex Algorithm 5A to compute an optimal solution to your standard form starting with all slacks basic. (d) Plot your progress in part (c) on the graph of part (a).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 2CEXP
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First 3 parts are solved.

5-28 Consider the linear program
max x1 + x2
s.t. x1 + x2 ≤ 9
-2x1 + x2 ≤ 0
x1 - 2x2 ≤ 0
x1, x2 ≥ 0
(a) Solve the problem graphically.
(b) Add slacks x3,c, x5 to place the model
in standard form.
(c) Apply rudimentary simplex Algorithm 5A
to compute an optimal solution to your
standard form starting with all slacks basic.
(d) Plot your progress in part (c) on the
graph of part (a).
(e) How can the algorithm be making progress when l = 0 if some moves of part
(c) left the solution unchanged? Explain.
5-29 Do Exercise 5-28 for the LP
max x1
s.t. 6x1 + 3x2 ≤ 18
12x1 - 3x2 ≤ 0
x1, x2 ≥ 0

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