Problem:

Consider the following problem

Maximize Z= 3x1 +5x2 +6x3

subject to

2x1 +x2+ x3 <_4

x1 +2x2 +x3 <_4

x1 +x2 +2x3 <_4

x1 + x2 + x3 <_3

and, x1,x2,x3 >_ 0

Required:

Question 1) Work through the simplex metod step by step in algabraeic form

Question 2) Work through the simplex method in tabular form

Question 3) Use a computer package based on the simplex method to solve the problem.

Solve the given numerical problem and illustrate step by step calculation.