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Admittedly, this is a homework question but I just want to make sure my understanding of it is correct. I have the following:

Maximize $z = x_{1}$

$5x_{1} + x_{2} = 4$

$6x_{1} + x_{3} = 8$

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

where $x_{1}, x_{2}, x_{3}, x_{4} \geq 0$

Solve the problem by inspection (do not use Gauss-Jordan row ops).

From what I see, this simply means that we have to increase $x_{1}$ to mazimize z so long as the constraints are met. I believe we can also do away with constraint 3 since it is redundant? However, the constraints were given as inequalities. I'm a bit confused as to how the answer is supposed to look if I am not alloed to derive new rows from this. $x_{2}, x_{3}, x_{4}$ are of course slack variables

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HINT

Note that for each of the equalities, $x_1$ will need to be less the larger you make $x_2$ $x_3$ or $x_4.$ So try setting $x_2,x_3,x_4$ equal to zero. The smallest of the three values you get for $x_1$ will be the best you can do and you can always satisfy it.

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    Ah I see. I just needed to think about it differently. Thanks! – 2017-02-20