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Find all the basic solution of the following problem:

written 5.6 years ago by teamques10 ★ 68k

•   modified 5.6 years ago

Maximise:

$z=x_{1}+3x_{2}+3x_{3}$

subject to,

$x_{1}+2x_{2}+3x_{3}=4$

$2x_{1}+3x_{2}+5x_{3}=7$

$x_{1}, \ x_{2}, \ x_{3} \ge 0$

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written 5.6 years ago by teamques10 ★ 68k

Solution:

Sr. No.	Non Basic Variable	Basic Variable	Equation and the values of the basic variable	Value of z	Is the solution basic?
1	$x_{3}=0$	$x_{1}, \ x_{2}$	$x_{1}+2x_{2}=4 \\ 2x_{1}+3x_{2}=7 \\ x_{1}=2, \ x_{2}=1$	5	Yes
2	$x_{2}=0$	$x_{1}, \ x_{3}$	$x_{1}+3x_{3}=4 \\ 2x_{1}+5x_{3}=7 \\ x_{1}=1, \ x_{3}=1$	4	Yes
3	$x_{1}=0$	$x_{2}, \ x_{3}$	$2x_{2}+3x_{3}=4 \\ 3x_{2}+5x_{3}=7 \\ x_{2}=-1, \ x_{3}=2$	-	No

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