Consider the following problem

Max. Z = 2x₁ + 5x₂ + 3x₃

s.t. vx₁ - 2x₂ + x₃ 20

2x₁ + 4x₂ + x₃ = 50

x₁, x₂, x₃ 0

Select the correct answer for the following questions

i. Construct the starting simplex table

ii. Identify the initial artificial basic feasible solution

iii. Identify the entering basic variable and the leaving basic variable

--------------------

answer:

Starting simplex table

Basic Variable	Z	x1	x2	x3	R	a1	a2	Soln.
Z	1	-3M-2	-2M-5	-2M-3	M	0	0	-70M
a1	0	1	-2	1	-1	1	0	20
a2	0	2	4	1	0	0	1	50

Initial artificial basic feasible solution: x₁ = 0, x₂ = 0, x₃ = 0, a₁ = 20, a₂ = 50

Entering basic variable: x₁ enters the basis

Leaving basic variable: a₁ leaves the basis

Starting simplex table

Basic Variable	Z	x1	x2	x3	R	a1	a2	Soln.
Z	1	-3M-2	-2M-5	-2M-3	M	0	0	-70M
a1	0	1	-2	1	-1	1	0	20
a2	0	2	4	1	0	0	1	50

Initial artificial basic feasible solution: x₁ = 0, x₂ = 0, x₃ = 0, a₁ = 20, a₂ = 50

Entering basic variable: x3 enters the basis

Leaving basic variable: a₁ leaves the basis

Starting simplex table

Basic Variable	Z	x1	x2	x3	R	a1	a2	Soln.
Z	1	-2M-3	-5M-2	-3M-2	M	0	0	-70M
a1	0	1	-2	1	-1	1	0	20
a2	0	2	4	1	0	0	1	50

Initial artificial basic feasible solution: x₁ = 0, x₂ = 0, x₃ = 0, a₁ = 20, a₂ = 50

Entering basic variable: x2 enters the basis

Leaving basic variable: a2 leaves the basis