# Using the Simplex Method

Consider the following maximum problem in standard form:

Maximize Z = 8X1 + 2X2 + 3X3

Subject to the constraints

X1 + 3X2 + 2X3 < 10

4X1 + 2X2 + 3X3 < 8

X1 > 0, X2 > 0, X3 > 0

(a) Rewrite the two constraints as equations by adding slack variables S1 and S2.

(b) Set up the initial simplex tableau for this problem.

https://brainmass.com/math/linear-programming/122940

#### Solution Preview

Maximize Z = 8X1 + 2X2 + 3X3

subject to the constraints

X1 + 3X2 + 2X3 <= 10 Eq(1)

4X1 + 2X2 + 3X3 <= 8 Eq(2)

X1 >= 0, X2 >= 0, X3 >= 0

The complete solution, under proper formatting and containing tables, is provided in the attached file.

(a) Rewrite the two constraints as equations by adding slack variables S1 and S2.

Add one slack variable to each constraint. Let S1 be the slack variable in constraint eq(1) and S2 be the lack variable in constraint eq(2).

Constraints with slack variables are

X1 + 3X2 + 2X3 + S1 = 10 Eq(1)

4X1 + 2X2 ...

#### Solution Summary

This solution shows the two constraints as equations by adding slack variables S1 and S2 and the initial simplex tableau for the problem. All required calculations are provided and the full solution is provided within an attached Word document.