Chapter 6, Problem 1RE

To determine

The basic variable from the basic solution (B) given in the table.

Answer to Problem 1RE

In basic solution (B), the basic variables are $\underset{\_}{x_2\text{and }{s}_2}$ the non-basic variables are $x_1\text{ and }{s}_1$.

Explanation of Solution

The given linear equations are:

$\begin{array}{c}2x_1+5x_2+s_1=32\\ x_1+2x_2+s_2=14\end{array}$

The given table of six basic solutions to the e-system is:

	$x_1$	$x_2$	$s_1$	$s_2$
(A)	0	0	32	14
(B)	0	6.4	0	1.2
(C)	0	7	–3	0
(D)	16	0	0	–2
(E)		0		0
(F)			0	0

The classification of variables are basic or non-basic depends on the basic solution. For the non-basic variable zero is assigned and basic variables have non-zero values.

The basic solution (B) of above table shows the basic solution $(x_1,x_{2,},s_1,s_2)=\left(0,\text{6}.\text{4},0,\text{1}.\text{2}\right).$

Hence, for (B), the basic variables are $\underset{\_}{x_2\text{and }{s}_2}$ the non-basic variables are $x_1\text{ and }{s}_1$.