Use Dual Simplex Method to solve the following problem:

Maximize z = -2x₁ -3x₂

subject to:

x₁ + x₂ ≥ 2

2x₁ + x₂ ≤ 10

x₁ + x₂ ≤ 8

x₁, x₂ ≥ 0

Maximize z = -2x₁ – 3x₂

Check all the options one by one and put the value and find in which we are getting the maximum value which is also satisfying the given equations form.

Option 1: x​₁​ = 6, x₂​ = 2 and z = -18

Here, z is -18

x₁​ + x₂​ ≥ 2                      / 6+ 2 ≥ 2 or 8 ≥ 2 [true]

2x​₁​ + x₂​ ≤ 10                 / 2*6 + 2 <=10 or 10<=10  [true]

x​₁​ + x₂​ ≤ 8                     / 6 + 2 <=8  or 8<=8     [true]

Also, x₁ and x₂ are >= 0

Option 2:  x₁​ = 2, x₂​ = 6 and z = -22

Z = -2x​₁​ -3x₂             / z = -4 – 18 = -22

x₁​ + x₂​ ≥ 2                      / 2+ 6 ≥ 2 or 8 ≥ 2 [true]

2x​₁​ + x₂​ ≤ 10                 / 2*4 + 6 <=10 or 10<=10  [true]

x​₁​ + x₂​ ≤ 8                     / 2 + 6 <=8  or 8<=8     [true]

Also, x₁ and x₂ are >= 0