6. Solve the following Transportation Problem:D1D2D3S1113643S2603551S32012487271849233Requirementa) Find the Initial Basic Feasible Solution using Vogel's Approximation Method (VAM).b) Check optimality of the solution [find improvement indices] using MODI method.D42344Sources188

The following steps are used to obtain the optimal solution of the transportation problem. To…

Answered: 6. Solve the following Transportation…

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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Calculate the expected value for the given probability distribution. 1 7 12 p(x) 0.4 0.13 O not possible to do from the information provided O 6.2 5.25 2.5
The oil company has three refineries located throughout the country with production capacity (120, 70 and 50) tons. Each day the company must supply its four customers with high purity gasoline with at least (60, 40, 30 and 110) tons. The transportation costs (in $) are given below. Obtain an initial basic feasible solution using Vogel's approximation model. Origin Destination A В 1 20 22 17 4 2 24 37 9. 7 3 32 37 20 15
Solve this LP max z = 3x1 + 2x2 +2.5x3 8.t. x1 + x2 + 2x3 201 +203 1, 2, 3 > 0 has optimal tableau So B= <4 <6 = Z 21 X2 1 0 0 0 0 0 1 T3 C3 1 ā13 0 ā23 82 ₂ 1/2 1 0 ā 13 ā23 5₁ ; 5₂ = [ and the optimal solution for zis z = Now find the maximum amount A that the optimal BV remains optimal. 81 -188--18:3 and = and using B-¹ and Bcy formulas the missing values in optimal tableau are €3=0; €₂=0; rhs IN L -1/2 by 1/2 ba and cgy -[00] that the value of c3 can be increased so
• Consider the following LP: maximize 2x1 + 5x2 s.t. -x1 + 2x2 < 5 2x1 + 3x2 < 12 X1 + x2 2 -1 X1, X2 2 0 1. Write the dual problem. 2. Solve the optimal solution for the primal problem. 3. Find the optimal dual solutions by complementary slackness.
c. Find the initial feasible solution using. VAM method. TO From Supply 3 4 300 II 2 6. 9. 400 III 8. 3 500 Demand 250 350 400 200 a22 53
Justify your answer using complementary slackness and if given solution is optimal give the optimal solution to the dual too
The table below shows the cost of transporting a unit item in the given routes; FROM/TO 1 2 3 4 SUPPLY 10 8 12 0 100 6 7 4 0 150 10 9 6 0 250 DEMAND 12080 200 100 A B a) A basic feasible solution is obtained using LCM as a11, x12, X23, 231, X33 , X34. Obtain the basic variables. T11= * 12 = 223 = 231 = T33 = 234 = b) A basic feasible solution is obtained using VAM as 11, *12, T23, X31, T 33 , X34. Obtain the basic variables. I14= 221 = 223 = T32 = 233 = c) Between the two solutions, which one has the least cost?
2. Apply the principle of duality to solve the following LPP. Minimise subject to Z=4x1 + x2 3x1 + x2 = 3 4x13x26 x12x24 x1, x2 0.
Consider the following LPP: Min Z = 3X1 + X2 + X3 Such that: X1 – 2X2 + X3 3 which has the following optimum solution: Basic| X, Xz Х Ха Хъ R R2 Solution Z-5 -1 1- M -1-M X4 3 1 -2 -5 12 X2 1 -1 -2 1 X3-2 10 0 1 Then, the dual optimal solution (yı, Y2, Y3, w) %3D Select one: (0,1,-1,2) (-1,1,-1,2) (0,0,1,1) (0,1,0,2)

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