Perform the primal simplex method to solve the following LPs. The slack variables are the initial basic variables. Write the basis and the simplex tableau at each iteration. Fill in the blanks of the tableaux and the under-lined blanks.

Maximize 2 x₁ x₂ + x₃,

Subject to 3 x₁ + x₂ + x₃ 60,

x₁ x₂ + 2 x₃ 10,

x₁ + x₂ x₃ 20,

x₁ , x₂ , x₃ 0.

The Simplex Tableau with respect to B⁰ = {s₁, s₂, s₃}:

	x1	x2	x3	s1	s2	s3	Max
0th row	2	-1	1	0	0	0	Z 0	ratio
1st row	3	1	1	1	0	0	60
2nd row	1	-1	2	0	1	0	10
3rd row	1	1	-1	0	0	1	20

What is the objective value? What is the basic feasible solution? Is the basis optimal?

1-2 (Contnued) The Simplex Tableau with respect to B¹ = { }:

	x1	x2	x3	s1	s2	s3	Max
0th row								ratio
1st row
2nd row
3rd row

What is the objective value? What is the basic feasible solution? Is the basis optimal?

The simplex Tableau with respect to B² = { }:

	x1	x2	x3	s1	s2	s3	Max
0th row								ratio
1st row
2nd row
3rd row

What is the objective value? What is the basic feasible solution? Is the basis optimal?