Problem 7-13Recall the Martin-Beck Company distribution system problem shown below.Min 5x11 + 2x2 + 3x13 + 4x21 + 3x22 + 4x23 + 9x31 + 7x32 + 5x3z + 10x41 + 4x42+ 2x43 + 8x51 + 4x52 + 3x53 + 175yı + 300y2 + 375y3 + 500y4s.t.< 10y Detroit capacity< 20y2 Toledo capacity< 30y; Denver capacity< 40y4 Kansas City capacitySt. Louis capacityElx + 7ix + IxX21 + x22 + x23X31 + x32 + x33X41 + x42 + X43X51 + X52 + X53< 30XI1 + x21 +x31 + x41 + rSı= 30Boston demandx12 + x22 + x32 + x42 + x52= 20Atlanta demandx13 + x23 + x33 + x43 + xs3= 20Houston demandX; 2 0 for all i and j; yı, y2. y3. y4 = 0, 1 a. Modify the formulation shown above to account to the policy restriction that one plant, but not two, must be located either in Detorit or in Toledo. Note: all answers should be whole numbers.New Optimal Solution:211 =212 =X213 =221 =*22 =223 =231 =20132 =233 =10X241 =142 =43 =251 =252 =20X253 =10Y1 =1Y2 =Y3 =Y4 =Value =940

Name: Problem 7-13Recall the Martin-Beck Company distribution system proble
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Description: Problem 7-13Recall the Martin-Beck Company distribution system problem shown below.Min 5x11 + 2x2 + 3x13 + 4x21 + 3x22 + 4x23 + 9x31 + 7x32 + 5x3z + 10x41 + 4x42+ 2x43 + 8x51 + 4x52 + 3x53 + 175yı + 300y2 + 375y3 + 500y4s.t.< 10y Detroit capacity< 2

For simplicity, let us use y1=1, y2=0, y3=1, and y4=0 as shown in the green tick mark for simplicity…

Math

Advanced Math

Recall the Martin-Beck Company distribution system problem shown below. Min 5x1 + 2x12 + 3x13 + 4x21 + 3x22 + 4x23 + 9x31 + 7x32 + 5x33 + 10x41 + 4x42 + 2x43 + 8r5ı + 4x52 + 3xs3 + 175yı + 300y2 + 375y3 + 500y4 s.t. < 10yı Detroit capacity < 20y2 Toledo capacity s 30yz Denver capacity < 40y4 Kansas City capacity < 30 St. Louis capacity X1 + x12 + x13 x21 + x22 + x23 X31 + x32 + x33 X41 + x42 + x43 X51 + X52 + x53 XI1 + x21 +x31 + x41 + x51 = 30 Boston demand = 20 = 20 Xj 2 0 for all i and j; yı, y2. y3, y4 = 0, 1 X12 + x22 + x32 + x42+ x52 Atlanta demand x13 + x23 + x33 + x43 + x53 Houston demand

Recall the Martin-Beck Company distribution system problem shown below. Min 5x1 + 2x12 + 3x13 + 4x21 + 3x22 + 4x23 + 9x31 + 7x32 + 5x33 + 10x41 + 4x42 + 2x43 + 8r5ı + 4x52 + 3xs3 + 175yı + 300y2 + 375y3 + 500y4 s.t. < 10yı Detroit capacity < 20y2 Toledo capacity s 30yz Denver capacity < 40y4 Kansas City capacity < 30 St. Louis capacity X1 + x12 + x13 x21 + x22 + x23 X31 + x32 + x33 X41 + x42 + x43 X51 + X52 + x53 XI1 + x21 +x31 + x41 + x51 = 30 Boston demand = 20 = 20 Xj 2 0 for all i and j; yı, y2. y3, y4 = 0, 1 X12 + x22 + x32 + x42+ x52 Atlanta demand x13 + x23 + x33 + x43 + x53 Houston demand

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 7-13
Recall the Martin-Beck Company distribution system problem shown below.
Min 5x11 + 2x2 + 3x13 + 4x21 + 3x22 + 4x23 + 9x31 + 7x32 + 5x3z + 10x41 + 4x42
+ 2x43 + 8x51 + 4x52 + 3x53 + 175yı + 300y2 + 375y3 + 500y4
s.t.
< 10y Detroit capacity
< 20y2 Toledo capacity
< 30y; Denver capacity
< 40y4 Kansas City capacity
St. Louis capacity
Elx + 7ix + Ix
X21 + x22 + x23
X31 + x32 + x33
X41 + x42 + X43
X51 + X52 + X53
< 30
XI1 + x21 +x31 + x41 + rSı
= 30
Boston demand
x12 + x22 + x32 + x42 + x52
= 20
Atlanta demand
x13 + x23 + x33 + x43 + xs3
= 20
Houston demand
X; 2 0 for all i and j; yı, y2. y3. y4 = 0, 1

a. Modify the formulation shown above to account to the policy restriction that one plant, but not two, must be located either in Detorit or in Toledo. Note: all answers should be whole numbers.
New Optimal Solution:
211 =
212 =
X
213 =
221 =
*22 =
223 =
231 =
20
132 =
233 =
10
X
241 =
142 =
43 =
251 =
252 =
20
X
253 =
10
Y1 =
1
Y2 =
Y3 =
Y4 =
Value =
940

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