Solve the Linear Programing problem Minimize z 8x1 10x2 1

Solve the Linear Programing problem

Minimize: z = 8x₁ + 10x₂ + 11x₃ + 14x₄

ST:
x₁ = .03A + .02B + .01C
x₂ = .06A + .04B + .01C
x₃ = .10A + .03B + .04C
x₄ = .12A + .09B + .04C

0 <= A <= 80   0 <= B <= 40   0 <= C <= 20

Solution

Since A, B and C can take the minimum values of 0, the minimum value of x1,x2,x3,x4 will also be 0.

Putting this in objective function the minimum value we get is 0.