Question

Consider the following LP problem:

Minimize Cost = 3x₁ + 2x₂

s.t.

1x₁ + 2x₂ ≤ 12

2x₁ + 3 x₂ = 12

2 x₁ + x₂ ≥ 8

x₁≥ 0,

x₂ ≥ 0

What is the optimal solution of this LP?

(0,8)(12,0)(4,0)(0,4)(2,3)(0,6)(3,2)

I NEED SOLUTION!

Answer 1

The constraint equations are plotted on graph as shown below:

The red shaded region (left of red line) indicates the first constraint, and the green shaded region (right of green line) indicates the third constraint. The overlapping region is in our consideration.

Now, the blue line indicates the second (equality) constraint.

Hence, the feasible solutions lie along the blue line between the points (3,2) and (6,0)

Value of objective function at (3,2) = 3x3 + 2x2 = 13

Value of objective function at (6,0) = 3x6 + 2x0 = 18

Minimum value is at (3,2).