Graphical Solution Problems
1. For the linear program
Max z = 3x1 + 3x2
Subject to:
x1 + 3x2 < 12
3x1 + x2 > 12
x1 – x2 = 2
x1, x2 > 0
1) Show the feasible region.
2) Find the optimal solution using the graphical solution procedure. What is the value of the objective function?
2. Consider the following linear programming problem:
Min z = 3x1 + 2x2
Subject to:
2x1 + x2 > 12
x1 + x2 > 10
2x2 < 8
x1, x2 > 0
1) Solve the problem using the graphical solution procedure.
2) What are the values of the slack and surplus variables at the optimal solution?
3) What happens to the problem if the objective function is changed to
Max z = 3x1 + 2x2 ?
3. Solve the following linear programming problem graphically.
Max z = 5x1 + 7x2
Subject to:
2x1 + 3x2 < 6
x1 > 5
x1, x2 > 0
4. Solve the following linear programming problem graphically.
Min z = 4x1 + 2x2
Subject to:
2x1 + x2 > 400
3x1 + 3x2 < 900
x2 > 50
x1, x2 > 0
Answers:
1. 1) The feasible region consists of a line segment 2) Max z = 21
2. 1) Min z = 26 2) s1 = 4, s2 = 0, s3 = 0 3) Unbounded problem
3. Infeasible problem
4. Alternative optimal solutions. Min z = 800