Can you show the graph and everything. Problem

$2($

Graphical method

$)(30$

$$pts

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Use the graphical method to solve the following linear program:

max

$6$

x

$1$

$+$

$4$

x

$2$

subject to x

$1$

$+$

$2$

x

$2$

$<$

$=$

$8$

$3$

x

$1$

$+$

$2$

x

$2$

$<$

$=$

$18$

x

$2$

$<$

$=$

$3$

x

$1$

$,$

$$x

$2$

$>$

$=$

$0$

$.$

i

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$$Find the tight constraints at the optimal solution.

ii

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$$Solve the system of tight constraints to find the optimal solution.

iii. What is the optimal value?

iv

$.$

$$Find the slack

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surplus on loose constraints at the optimal solution.