Math Problem Solver

Instructions: Solve both questions using the simplex method. Show all

steps in your calculations, including the formation of initial and subsequent

simplex tableaux. Clearly state the optimal solution if one exists.

Questions

Question 1

Solve the following linear programming problem using the simplex method.

1. Maximize Z = 3x1 +5x2

subject to

2x1 +3x2 ≤ 12,

x1 +x2 ≤5,

x1,x2 ≥ 0.

• Set up the initial simplex tableau for this problem.

• Perform the necessary pivot operations to reach the optimal solution.

• Clearly state the values of x1, x2, and Z at the optimum.

Question 2

Solve the following linear programming problem using the simplex method.

1. Minimize Z = 4x1 +6x2 +3x3

subject to

x1 +2x2 +x3 ≥8,

2x1 +x2 +3x3 ≥ 12,

x1,x2,x3 ≥ 0.

• Convert the problem into standard form by introducing slack variables.

• Set up the initial simplex tableau and determine the starting basic feasible

solution.

• Perform the simplex algorithm steps to minimize Z.

• Clearly state the values of x1, x2, x3, and Z at the optimal solution