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I am stuck in the following problem:

maximize z=$x_1+2x_2+3x_3-4x_4$

subject to

$2x_1+3x_2-x_3-x_4=15$

$6x_1+x_2+x_3-3x_4=21$

$8x_1+2x_2+3x_3-4x_4=30$

$x_1,x_2,x_3,x_4$$\ge0$

then,$x_1=4,x_2=3,x_3=0,x_4=2$ is

(a) an optimal solution

(b)a degenerate basic feasible solution

(c)a non degenerate basic feasible solution

(d)a non basic feasible solution

the way i tried:

we have,4-3=1 non basic variable.so,equation $x_3$=0,we get the given solution as basic as well as non degenerate,so,according to me answer is (c)but answer is given to be (d).

any help would be appericiated

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    Where does it say that the answer is (d)? I also think it is a BFS. it is feasible and has 3 non-zero components, in a problem with 3 constraints. – 2017-02-04
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    @ Anna SdTC: but answer anyways is given to be (d) – 2017-02-04
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    Is it class notes? A textbook? Which one? Is there an errata published? – 2017-02-04
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    @ Anna SdTC:it is a problem from competetive exam in india – 2017-02-04
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    @ Anna SdTC:yes,the answer is (d).determinant of coefficients of constraints is zero, if we put $x_3$=0.so,the resulting system does not have a unique solution on putting $x_3$=0... – 2017-02-04

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