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1. Solve the following LP problem using SIMPLEX method

MINIMIZE Z = 5X1 - 2X2 +3X3

Subject to

2X1 + 2X2 - X3 >= 2

3X1 – 4X2 <= 3

X2 + 3X3 <= 5

X1 , X2 and X3 >= 0

2.a) Write the DUAL of the LP problem given the Problem - 1 and find out the solution of Dual problem from the final table of simplex (Primal).

(b) Discuss the differences between PRIMAL and DUAL.

(C) Explain the economic interpretation of DUAL variable.

The 1st constraint has a greater than or equal to sign rather than a less then or equal to,

so bring in the smallest value from the z-row to find which row to add.

The Z-row would have a -5 2 -3, so X3 would be the entering variable.

Constraint #3 is the only one with a positive value in that column,

so use X3 as the entering varialbe.

Add -1/3 * C3 to the Z row and C1, leave C2, and divide C3 by 3.

This should give the next tableau. Once this has been gotten to,

use X1 as the entering basic variable in constraint 3.

This should have x3 as 5/3, which satisfies the 1st constraint.

The 2nd constraint isn't satisfied yet, so keep trying to minimize the answer.

The next element to add would be x1, using row 3.

Once this has been done, the Z row has all positive coefficients and

the 1st constraint is satisfied, so the problem is done.

It should look like

-5 2 -3 0 0 0 0 0

2 2 -1 1 -1 0 0 2

3 -4 0 0 0 1 0 3

1 0 3 0 0 0 1 5

-4 2 0 0 0 0 1 5

2.3333 2 0 1 -1 0 0.3333 3.6667

3 -4 0 0 0 1 0 3

0.3333 0 1 0 0 0 0.3333 1.6667

0 2 12 0 0 0 5 25

0 2 -7 1 -1 0 -2 -8

0 -4 -9 0 0 1 -3 -12

1 0 3 0 0 0 1 5

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