assignment4(1)

# assignment4(1) - tableau and then to solve the original...

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ORIE 3300/5300 ASSIGNMENT 4 Fall 2011 Individual work. Due: 11am, Tuesday September 27. 1. Consider the following tableau for a linear program in standard equality form: z + 4 x 3 - 3 x 5 - 2 x 6 = 5 + 4 x 3 + x 4 + 3 x 5 + 2 x 6 = 6 x 2 + 2 x 3 - x 5 + 2 x 6 = 4 x 1 - 2 x 3 + 2 x 5 + x 6 = 2 . List all pairs ( k, r ) such that k could be the entering index and r could be the leaving index for an iteration of the simplex method starting from this tableau. 2. Transform the following linear program to an equivalent problem in standard equality form. (As discussed on p. 19–20 of Section 2 in the lectures notes, replace the free variable by a diﬀerence of two nonneg- ative variables.) Then use the simplex method, ﬁrst to ﬁnd a feasible
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Unformatted text preview: tableau, and then to solve the original problem. maximize-2 x 1 + 5 x 2-x 3 subject to x 1 + 2 x 2-3 x 3 ≥ 2 8 x 1 + 2 x 2-2 x 3 ≤ 12 x 1 , x 2 ≥ x 3 free . 3. Answer question 2-8(b) (on “input-output models”) in the AMPL book. 4. Required for ORIE 5300; Bonus question for ORIE 3300 Find an example of a tableau for a linear program in standard equality form, such that at least one of the reduced costs is strictly positive, and yet the corresponding basic solution is optimal. 1...
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