written 6.3 years ago by
teamques10
★ 64k
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• modified 4.0 years ago |
Find all basic solutions to the following problem
Max. $Z = x_1 +3x_2 + 3x_3, $
$\text{subject to} \hspace{0.2cm} x_1 + 2 x_2 +3 x_3=4; 2 x_1 +3x_2 +5 x_3=7$
$x_1, x_2, x_3 ≥ 0$
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written 6.2 years ago by
teamques10
★ 64k
|
Since there are three variables and two constraints, a basic solution can be obtained by putting 3 - 2 = 1 variable equals to zero & there will be $^3C_2= 3$ basic solutions.
| No. of basic solutions | Non – basic variables =0 | Basic variables | Equations and the values of the basic variables | Is the solution feasible | Is the solution degenerate? | Value of z | Is the solution optimal ? |
|---|---|---|---|---|---|---|---|
| 1. | $x_1$=0 | $x_2 , x_3$ | $2x_2 +3x_3 = 4,\\3x_2 +5x_3=7,\\x_2 = -1, x_3=2$ | No | No | 0 | No |
| 2. | $x_2$=0 | $x_1,x_3$ | $x_1 +3x_3=4,\\2x_1 +5x_3=7,\\x_1=1, x_3=1$ | Yes | No | 4 | No |
| 3. | $x_3$=0 | $x_1,x_2$ | $x_1 + 2x_2=4,\\2x_1+3x_2=7,\\x_1=2, x_2 =1$ | Yes | No | 5 | Yes |
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