Question

In: Advanced Math

Find dual from primal conversion MIN Z = x1 - 2x2 subject to 4x1 - x2 >= 8 2x1 + x2 >= 10 -x1 + x2 <= 7 and x1,x2 >= 0

Expert Solution

Find dual from primal conversion

MIN Z = x1 - 2x2

subject to

4x1 - x2 >= 8

2x1 + x2 >= 10

-x1 + x2 <= 7

and x1,x2 >= 0

all details are in belowPrimal is (Solution steps of Primal by Simplex method)

MIN Zx = x1 - 2 x2

subject to

4 x1 - x2 ≥ 8

2 x1 + x2 ≥ 10

- x1 + x2 ≤ 7

and x1,x2≥0;

Since objective function is minimizing, all ≤ constraints (3) can be converted to ≥ type by multipling both sides by -1

300

Nipun Maity answered 1 year ago

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1...

Find the Dual of the following LP max z = 4x1 − x2 + 2x3 x1 + x2 ≤ 5 2x1 + x2 ≤ 7 2x2 + x3 ≥ 6 x1 + x3 = 4 x1 ≥ 0, x2, x3 free

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.

Find the dual of the following LP, using direct method. minz=4X1 +2X2 -X3 subject to X1...

Find the dual of the following LP, using direct method. minz=4X1 +2X2 -X3 subject to X1 +2X2 ≤6 X1 -X2 +2X3 =8 X1 ≥0,X2 ≥0,X3 urs

Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2...

Max Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 ≤ 8 2x2 + 5x3 ≤ 12 3x1 + x2 + 4x3 ≤15 and x1,x2,x3≥0; Indicate clearly the optimal basic and nonbasic variables and their values and write the reduced cost of each optimal nonbasic variable.

MAX Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 <= 8 2x2...

MAX Z = 2x1 + 8x2 + 4x3 subject to 2x1 + 3x2 <= 8 2x2 + 5x3 <= 12 3x1 + x2 + 4x3 <= 15 x1 + x3 = 11 and x1,x2,x3 >= 0 apply the Dual Simplex Method to recover feasibility.

By using Big-m method Minimize z=4x1+8x2+3X3subject to x1+x2>=2, 2x1+x3>=5 and x1,x2,x3>=0

Given the following primal problem: maximize z = 2x1 + 4x2 + 3x3 subject to x1...

Given the following primal problem: maximize z = 2x1 + 4x2 + 3x3 subject to x1 + 3x2 + 2x3 ≥ 20 x1 + 5x2 ≥ 10 x1 + 2x2 + x3 ≤ 18 x1 , x2 , x3 ≥ 0 1. Write this LP in standart form of LP. 2.Find the optimal solution to this problem by applying the Dual Simplex method for finding the initial basic feasible solution to the primal of this LP. Then, find the optimal...

Find the dual problem for each of the following primal problems. a): min z=6x1+8x2 st: 3x1+x2>=4...

Find the dual problem for each of the following primal problems. a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0 b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4 x1<=0,x2<=0,x3 unrestricted

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which...

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional—marginal—unit of good 1.) 20. Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1( x1,x2)=1 and MU2( x1,x 2)=3. Then...

Solve the following linear programs graphically. Minimize Z = 4X1 - X2 Subject to X1 +...

Solve the following linear programs graphically. Minimize Z = 4X1 - X2 Subject to X1 + X2 ≤ 6 X1 - X2 ≥ 3 -X1 + 2X2 ≥ 2 X1, X2 ≥ 0