Solve by simplex method

1. Maximize Z = 5x₁ + 3x₂

Subject to

3x₁ + 5x₂ ≤ 15

5x₁ + 2x₂ ≤ 10

&         x₁ ≥ 0, x₂  ≥ 0

[Ans. Max Z = 235/19, x₁= 20/19, x₂= 45/19]

1. Maximize Z = 5x₁ + 7x₂

Subject to

x₁ + x₂ ≤ 4

3x₁ - 8x₂ ≤ 24

10x₁ + 7x₂ ≤ 35

&         x₁ ≥ 0, x₂  ≥ 0

[Ans. Max Z = 28, x₁= 0, x₂= 4]

1. Maximize Z = 2x₁ + 4x₂ + x₃+ x₄

Subject to

x₁ + 3x₂ + x₄ ≤ 4

2x₁ + x₂ ≤ 3

x₂ + 4x₃ + x₄ ≤ 3

&         x₁ ≥ 0, x₂  ≥ 0, x₃  ≥ 0, x₄  ≥ 0

[Ans. Max Z = 13/2, x₁= 1, x₂= 1, x₃= 1/2, x₄= 0]

1. Maximize Z = 7x₁ + 5x₂

Subject to

-x₁ - 2x₂ ≥ -6

4x₁ + 3x₂ ≤ 12

&         x₁ ≥ 0, x₂  ≥ 0

[Ans. Max Z = 21, x₁= 3, x₂= 0]

1. Maximize Z = 3x₁ + 2x₂

Subject to

2x₁ + x₂ ≤ 10

x₁ + 3x₂ ≤ 6

x₁ + x₂ ≤ 21

&         x₁ ≥ 0, x₂  ≥ 0