Carrington_hmwk6.docx - IE 534 Linear Programming Homework 6 \u2022 Assigned on Friday \u2022 Due by 10:00 AM(CST on Monday \u2022 Homework submitted at 10:01 AM

# Carrington_hmwk6.docx - IE 534 Linear Programming Homework...

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IE 534 Linear Programming Homework 6 Assigned on Friday 10/09/2015. Due by 10:00 AM (CST) on Monday 10/19/2015. Homework submitted at 10:01 AM or later will not be accepted. Submission can be in hard copy or by email as a single pdf document to lzw [email protected] 1. (10 points) The set of partitions of { 1 , 2 , ..., n + m} can be divided into the following regions. A+B+C+D: All possible partitions B+C+D: Basic partitions C+D: Feasible basic partitions D: Optimal basic partitions Consider the following LP. Transform it into max {c T max x 1 + 2 x 2 + 3 x 3 s . t . x 1 3 x 3 0 7 x 1 + 2 x 2 + 5 x 3 1 x 1 , x 2 , x 3 0 . x : A m × ( n + m ) x = b m × 1 , x ( n + m ) × 1 0 } , and answer these question s. ( n + m ) × 1 (a) How many partitions ( B, N ) of { 1 , 2 , ...n + m} are there with |B| = m, |N | = n ? 1
If m = 2 and n = 3, then (m + n) *n = (3 + 2) * 2 = 5 * 2 = 10 total partitions. (b) List all these partition. For each partition, identify one specific region (e.g., B is one region, B + C is not) that it belongs to. If a partition is basic, also give the basic solution and its objective value. Partition 1 >>dictionary dict = ' ' ' ' 'w4' 'x3' 'w5' 'zeta' [ 1] [ 6] [-20] [ -1] 'x1' [ 0] [ -1] [ 3] [ 0] 'x2' [0.5000] [3.5000] [-13] [-0.5000] Partition 2 >> dictionary dict = ' ' ' ' 'x2' 'w4' 'w5' 'zeta' [0.2308] [ 1.5385] [ 0.6154] [-0.2308] 'x1' [0.1154] [-0.2308] [-0.1923] [-0.1154] 'x3' [0.0385] [-0.0769] [ 0.2692] [-0.0385] Partition 3

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