e. Use VAM to obtain the initial solution for the transportation model below: Minimize Z = (21x11 +16x12 + 25.x13 +13x14) + (17x21 +18x22 +14x23 + 23.x24) + (32x31 + 27x32 +18x33 +41x34) Subject to Capacity constraints X11 + X12 + X13 + x14 = 11 Requirement constraints X11 + x21 + X31 = 6 X21 + x22 + x23 +x24 = 13 X12 + x22 + x32 = 10 X31 +X32 + X33 +x34 = 19 X13 +x23 +X33 = 12 X14 +X24 + X34 = 15 and y 2 0, for all i = 1,2,3,4 ; j = 1,2,3

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section6.5: Set-covering And Location-assignment Models
Problem 29P
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e. Use VAM to obtain the initial solution for the transportation model below:
Minimize Z = (21x11 +16x12 + 25.x13 +13x14)
+ (17x21 +18x22 +14x23 + 23x24)
+ (32x31 + 27x32 +18x33 +41x34)
Subject to
Capacity constraints
X11 + X12 + x13 + x14 =11
Requirement constraints
X11 +x21 + X31 = 6
X21 +x22 +x23 +x24 = 13
X12 +x22 +x32 = 10
X31 + X32 + X33 +X34 = 19
X13 + x23 +X33 = 12
X14 +x24 +x34 = 15
and *i 2 0, for all i = 1,2,3,4 ;j=1,2,3
Transcribed Image Text:e. Use VAM to obtain the initial solution for the transportation model below: Minimize Z = (21x11 +16x12 + 25.x13 +13x14) + (17x21 +18x22 +14x23 + 23x24) + (32x31 + 27x32 +18x33 +41x34) Subject to Capacity constraints X11 + X12 + x13 + x14 =11 Requirement constraints X11 +x21 + X31 = 6 X21 +x22 +x23 +x24 = 13 X12 +x22 +x32 = 10 X31 + X32 + X33 +X34 = 19 X13 + x23 +X33 = 12 X14 +x24 +x34 = 15 and *i 2 0, for all i = 1,2,3,4 ;j=1,2,3
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