I need help with the linear programming equations, I only need the ones marked wrong. Please show me your work and explain how to solve it. (ii) linear programming formulationLet Xijnumber of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem.Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.)Max 32x11 +34x12 + 32x13 +40x14+34x21 +30x22 +28x23 +38x24s.t.=Orders from Clifton SpringsOrders from DanvilleOrders from/for Dummy NodeOrders for D₁Orders for D2Orders for D3Orders for D4Xij≥ 0 for all i, j.1x11 + 1x12 + 1x13 + 1x14 ≤ 50001x21 + 1x22 + 1x23 + 1x24 ≤ 3000<x31+x322000+*33x33 + x34= 4000*12 +*22 ≤5000 01x13 + 1x23 + 1x33 = 300014+*24 ≤2000!! Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein'stwo plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be chargedbecause of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to thehighest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative.PlantClifton SpringsDanvillePlantClifton Springs2Danville1$32D₂Customer$34$34 $30The plant capacities and customer orders are as follows.Capacity (units)5,0003,000$32$2834$40$384Distributor Orders (units)D₁D₂D3D42,0005,0003,0002,000(a) Develop a network model and a linear programming formulation of this problem.

The main objective is to formulate the supply demand problem into linear programming problem.

) linear programming formulation Let x = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) 32x11 +34x12 +32x13 + 40x14 +34x21 +30x22 +28x23 +38x24 Max s.t. Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D₁ Orders for D₂ Orders for D3 Orders for D4 xij≥0 for all i, j. 1x11 + 1x12 1x21 + 1x22 x31 + 2000 + 1x13 + 1x14 ≤ 5000 + 1x23 + 1x24 ≤ 3000 *32 +*33 +*34 = 4000 *12+x22 ≤5000 X 1x13 + 1x23 + 1x33 = 3000 14+*24≤2000 X

) linear programming formulation Let x = number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem. Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.) 32x11 +34x12 +32x13 + 40x14 +34x21 +30x22 +28x23 +38x24 Max s.t. Orders from Clifton Springs Orders from Danville Orders from/for Dummy Node Orders for D₁ Orders for D₂ Orders for D3 Orders for D4 xij≥0 for all i, j. 1x11 + 1x12 1x21 + 1x22 x31 + 2000 + 1x13 + 1x14 ≤ 5000 + 1x23 + 1x24 ≤ 3000 32 +33 +34 = 4000 12+x22 ≤5000 X 1x13 + 1x23 + 1x33 = 3000 14+*24≤2000 X

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

I need help with the linear programming equations, I only need the ones marked wrong. Please show me your work and explain how to solve it.

(ii) linear programming formulation
Let Xij
number of units i shipped to client j, using the indices from the given table. (It may be necessary to combine plants or distributors in a single node in order to solve this problem.
Use index number 5 for this type of node. Enter "DNE" in any unused answer blanks.)
Max 32x11 +34x12 + 32x13 +40x14+34x21 +30x22 +28x23 +38x24
s.t.
=
Orders from Clifton Springs
Orders from Danville
Orders from/for Dummy Node
Orders for D₁
Orders for D2
Orders for D3
Orders for D4
Xij
≥ 0 for all i, j.
1x11 + 1x12 + 1x13 + 1x14 ≤ 5000
1x21 + 1x22 + 1x23 + 1x24 ≤ 3000
<
x31+x32
2000
+*33
x33 + x34
= 4000
*12 +*22 ≤5000 0
1x13 + 1x23 + 1x33 = 3000
14+*24 ≤2000
!
!

Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's
two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged
because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the
highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative.
Plant
Clifton Springs
Danville
Plant
Clifton Springs
2
Danville
1
$32
D₂
Customer
$34
$34 $30
The plant capacities and customer orders are as follows.
Capacity (units)
5,000
3,000
$32
$28
3
4
$40
$38
4
Distributor Orders (units)
D₁
D₂
D3
D4
2,000
5,000
3,000
2,000
(a) Develop a network model and a linear programming formulation of this problem.

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