The following LP formulation represents a transportation problem where raw material (in tons) from Supplier i, i={1,2,3} to Plant j, j={1,2,3). The problem is solved and the optimal objective function 5200. Using the sensitivity report shown below, what would be the optimal total cost if the cost of transporting 1 ton from Supplier 1 to Plant 1 becomes 2 and the cost of transporting 1 ton from Supplier 3 to Plant 3 becomes 2.5? Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 +4x22 +4.8x23 +3.5x31+3.6x32+3.2x33 Subject to x31+x32+x33 <= 500 x11+x21 + x31 = 500 x12+x22+x32 = 700 x13+x23+x33 = 600 xij<=200, for i= {2,3} &j= {1, 2, 3} xij >= 0, for i= {1,2,3} &j= {1, 2, 3}
The following LP formulation represents a transportation problem where raw material (in tons) from Supplier i, i={1,2,3} to Plant j, j={1,2,3). The problem is solved and the optimal objective function 5200. Using the sensitivity report shown below, what would be the optimal total cost if the cost of transporting 1 ton from Supplier 1 to Plant 1 becomes 2 and the cost of transporting 1 ton from Supplier 3 to Plant 3 becomes 2.5? Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 +4x22 +4.8x23 +3.5x31+3.6x32+3.2x33 Subject to x31+x32+x33 <= 500 x11+x21 + x31 = 500 x12+x22+x32 = 700 x13+x23+x33 = 600 xij<=200, for i= {2,3} &j= {1, 2, 3} xij >= 0, for i= {1,2,3} &j= {1, 2, 3}
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![The following LP formulation represents a transportation problem where raw material (in tons]
from Supplier i, i={1,2,3} to Plant j, j={1,2,3). The problem is solved and the optimal objective function value is
5200. Using the sensitivity report shown below, what would be the optimal total cost if the cost of
transporting 1 ton from Supplier 1 to Plant 1 becomes 2 and the cost of transporting 1 ton from
Supplier 3 to Plant 3 becomes 2.5?
Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 +4x22+4.8x23 +3.5x31+3.6x32+3.2x33
Subject to
x31+x32+x33 < 500
x11+x21 + x31 = 500
x12+x22 + x32 = 700
x13 + x23+x33 = 600
xij<=200, for i= {2,3} &j= {1, 2, 3}
xij >= 0, for i= {1,2,3} &j= {1, 2, 3}
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase Decrease
Name
500
1
2.5
1E+30
700
3
0.6
1E+30
200
1E+30
0.2
0
2.5
0
1E+30
1E+30
0.2
1E+30
1
1E+30
200
2.5
0
1E+30
0.6
1.8
1E+30
Variables
X11
X12
X13
X21
X22
X23
X31
X32
X33
10
200
000000000
5
3.5
4
4.8
3.5
3.6
3.2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19e658ec-7f66-4445-a198-3cbf9bcc9233%2Fdbb93226-6a25-4f37-8571-8cd68c3d2c39%2Fyffy028_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following LP formulation represents a transportation problem where raw material (in tons]
from Supplier i, i={1,2,3} to Plant j, j={1,2,3). The problem is solved and the optimal objective function value is
5200. Using the sensitivity report shown below, what would be the optimal total cost if the cost of
transporting 1 ton from Supplier 1 to Plant 1 becomes 2 and the cost of transporting 1 ton from
Supplier 3 to Plant 3 becomes 2.5?
Min Total cost = 1x11 + 3x12 + 5x13 +3.5x21 +4x22+4.8x23 +3.5x31+3.6x32+3.2x33
Subject to
x31+x32+x33 < 500
x11+x21 + x31 = 500
x12+x22 + x32 = 700
x13 + x23+x33 = 600
xij<=200, for i= {2,3} &j= {1, 2, 3}
xij >= 0, for i= {1,2,3} &j= {1, 2, 3}
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase Decrease
Name
500
1
2.5
1E+30
700
3
0.6
1E+30
200
1E+30
0.2
0
2.5
0
1E+30
1E+30
0.2
1E+30
1
1E+30
200
2.5
0
1E+30
0.6
1.8
1E+30
Variables
X11
X12
X13
X21
X22
X23
X31
X32
X33
10
200
000000000
5
3.5
4
4.8
3.5
3.6
3.2
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