(a) What basic feasible solution does this tableau represent? Is this solution optimal? Why or why not? (b) Does this tableau represent a unique optimum? If not, find an alternative optimal solution.

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4. Consider the linear program
max z =
5x1 + 3x₂ + x3
s.t.
X1 + X₂ + X3 ≤ 6
5x1 + 3x₂ + 6x3 ≤ 15
X1, X2, X3 ≥ 0
and an associated tableau is as follows:
Z
1
0
0
x1
0
0
1
x2
0
0.4
0.6
x3
5
-0.2
1.2
s1
0
1
0
s2
1
-0.2
0.2
RHS
15
3
3
(a) What basic feasible solution does this tableau represent? Is this solution optimal?
Why or why not?
(b) Does this tableau represent a unique optimum? If not, find an alternative optimal
solution.
Transcribed Image Text:4. Consider the linear program max z = 5x1 + 3x₂ + x3 s.t. X1 + X₂ + X3 ≤ 6 5x1 + 3x₂ + 6x3 ≤ 15 X1, X2, X3 ≥ 0 and an associated tableau is as follows: Z 1 0 0 x1 0 0 1 x2 0 0.4 0.6 x3 5 -0.2 1.2 s1 0 1 0 s2 1 -0.2 0.2 RHS 15 3 3 (a) What basic feasible solution does this tableau represent? Is this solution optimal? Why or why not? (b) Does this tableau represent a unique optimum? If not, find an alternative optimal solution.
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