(Simplex Method)

1.        Maximize Z = 10x1 + 5x2 subject to

4x1 + 5x2  \<100

5x1 + 2x2  \<80

x1 >/  0, x2  >/0

(Ans :  x1 = 200/17, x2 = 180/17 and maximum Z =2900/17 )

2.        Maximize Z = x1 + 4x2 + 5x    (Constraints, 3 variables and all are  type)

Subject to    3x1 + 3x3 \< 22

x1 + 2x2 + 3x3  \<14

3x1 + 2x2  \<14

x1, x2, x3 >/ 0

(Ans :  x1 = 0, x2 = 7, x3 = 0  and maximum profit Z = 28)

3.        Maximize Z = 40x1 + 24x    Total cost

Subject to    20x1 + 50x2  >/4800

80x1 + 50x2 + 3x3 >/ 14

x1, x2 >/ 0

(Ans :  x1 = 0, x2 = 144, S1 = 2400, S2 = 0    and Z = 24 x 144 = 3456 `)

4.        Solve the following Linear Programming problem by Simplex Method using the artificial variables.

Maximize Z = 3x1 + 5x

Subject to    x1 + x3 = 4

x2 + x4 = 0

3x1 + 2x2 + x5 = 12

x1, x2, x3, x4, x5 >/ 0

(Ans :  There is degeneracy in the solution because one of the variable in the basis is   x4 = 0, which is zero.)

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