1. work through the simplex method (in tabular form) step by step to solve the following problem:

Maximize: Z = 3x₁ + 4x₂ + 5x₃

st.: 3x₁+x₂+5x₃ 150

x₁+4x₂+x₃ 120

2x₁+2x₃ 105

x₁, x₂ , x₃ 0

This is what I have:

Max Z = 3x₁ + 4x₂ + 5x₃ + (0)x₄ + (0)x₅ + (0)x₆

st.: 3x₁+x₂+5x₃ +x₄=150

x₁+4x₂+x₃ +x₅ =120

2x₁+2x₃ + x₆ =105

x₁, x₂ , x_{3 ,} x4, x5, x6 0

And I made a table

I think we should do the ration test but I don't really know why I should choose x3

			3	4	5	0	0	0
Cj	BV	b	x1	x2	x3	x4	x5	x6	= b/x1
0		150	3	1	5	1	0	0	30
0		120	1	4	1	0	1	0	120
0		105	2	0	2	0	0	6	52.5