Appendix 2

Appendix II

Final Linear Programming Tableaus for Problems 2-A, 2-B, 2-C

FINAL LINEAR PROGRAMMING TABLEAU FOR PROBLEM 2-A

Row	x₀	t₁₂	t₂₂	t₃₂	x₁	x₂	x₃	x₄	x₅

0	1								-73.76
1					1
2		1
3						1			0.43
4			1
5							1		-1.70
6				1
7									0.35
8									-0.43
9									1.70
10								1	-0.35

Row	t₁₁	t₂₁	t₃₁	s₁	s₂	s₃	s₄	=

0	-347.5	-273.75	-51.11	293.33				293.33b₁
1				1.00				1.00b₁
2								0
3	-1.15	0.43	0.06	1.20				1.20b₁
4								0
5	-3.40	-1.70	0.74	4.00				4.00b₁
6								0
7	0.71	0.35	0.05	-0.67			1	b₄-0.67b₁
8	1.15	-0.43	-0.06	-1.20	1			b₂-1.20b₁
9	3.40	1.70	-0.74	-4.00		1		b₃-1.40b₁
10	-0.71	-0.35	-0.05	0.67				0.67b₁

FINAL LINEAR PROGRAMMING TABLEAU FOR PROBLEM 2-B

Row	x₀	t₁₂	t₂₂	t₃₂	x₁	x₂	x₃	x₄	x₅

0	1								-177.77
1					1				0.35
2		1
3						1
4			1
5							1		-3.12
6				1
7									0.35
8									0.59
9									3.12
10								1	-0.59

Row	t₁₁	t₂₁	t₃₁	s₁	s₂	s₃	s₄	=

0	-66.65	-377.77	-66.69		244.44			244.44b₂
1	-0.95	-0.35	-0.05		0.83			0.83b₂
2	1.00							0
3					1.00			1.00b₂
4		1.00						0
5	0.42	-3.12	0.53		3.33			3.33b₂
6			1.00					0
7	-0.96	0.35	0.05	1	-0.83			b₁-0.83b₂
8	0.07	0.59	0.09		-0.56		1	b₄-0.56b₂
9	-0.43	-3.12	-0.53		-3.33	1		b₃-3.33b₂
10	-0.07	-0.59	-0.09		0.56			0.56b₂

FINAL LINEAR PROGRAMMING TABLEAU FOR PROBLEM 2-C

Row	x₀	t₁₂	t₂₂	t₃₂	x₁	x₂	x₃	x₄	x₅

0	1								51.07
1					1				0.43
2		1
3						1			0.93
4			1
5							1
6				1
7									-0.43
8									-0.93
9									0.07
10								1	-0.07

Row	t₁₁	t₂₁	t₃₁	s₁	s₂	s₃	s₄	=

0	-97.89	-148.92	-105.93			73.33		73.33b₃
1	0.85	0.43	-0.19			0.25		0.25b₃
2	1.00							0
3	-0.13	0.93	-0.16			0.30		0.30b₃
4		1.00						0
5						1.00		1.00b₃
6			1.00					0
7	-0.85	-0.43	0.19	1		-0.25		b₁-0.25b₃
8	0.13	-0.93	0.16		1	-0.30		b₂-0.30b₃
9	0.14	0.07	0.18			-0.17	1	b₄-0.17b₃
10	-0.14	-0.07	-0.18			0.17		0.1667b₃