Question

Consider the following linear programming problem

Maximize 6x1 + 4x2 + 5x3

Subject to:

2x1 + 3x2 + x3 ≥ 30

2x1 + x2 + x3 ≤ 50

4x1 + 2x2 + 3x3 ≤ 120

x1, x2, x3 ≥ 0

a) Find the optimal solution by using simplex method

b) Find the dual price for the first constraint.

c) Find the dual price for the second constraint.

d) Find the dual price for the third constraint.

e) Suppose the right-hand side of the third constraint is increased from 120 to 125. Find the new optimal

solution and its value.

f) Suppose the right-hand side of the third constraint is decreased from 120 to 110. Find the new optimal

solution and its value.

Answer 1

a)

Optimal solution is determined using Simplex method as follows:

---------------------------------------------------------------------

b)

Refer the optimal tableau (iteration 4)

Value in the last (Cj-Zj) are the negatives of dual prices.

Value in last row and S1 column is 0

So, dual price for the first constraint is 0

---------------------------------------------------------------------

c)

Dual price for the second constraint is 2

---------------------------------------------------------------------

d)

Dual price for the third constraint is 1

---------------------------------------------------------------------