Seminar 2:
The simplex method for LP problems, MS Excel Solver,
sensitivity analysis
Problem 1: Use the simplex method to solve the problems:
a) z = 36x1 + 12x2 + 60x3 → max.
subject to
2x1 + x2 + 3x3 ≤ 9
x1 + 3x3 ≤ 3
x1, x2, x3 ≥ 0
b) z = x1 + 2x2 → max.
subject to
x1 − x2 ≤ 12
−2x1 + x2 ≤ 8
x1, x2, ≥ 0
c) z = 3x1 − x2 → max.
subject to
3x1 + x2 ≤ 3
3x1 − 4x2 ≥ 12
−2x1 + x2 ≥ 6
x1, x2, ≥ 0
Problem 2: Solve Problem 1 of Seminar 1 using computer.
Problem 3: Use Excel Solver to check the solution of the problem 1a)
Supplementary Tasks:
• Find intervals of stability for prices and capacities in Solver Sensitivity
report.
• Formulate the dual problem.
• Find the solution of the dual in the Solver Reports.
• Find the solution of the dual in the simplex table.
• Solve the dual problem and compare the optimal values of primal and dual
problems.