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question-1-max-ax-1-9x-2-4x-1-ax-2-lt-12-x-1-x-2-lt-a-x-1-gt-0-x-2-gt-0-ainr-pa595

Question 1

```
max,ax_(1)+9x_(2)
,4x_(1)+ax_(2)<=12
,x_(1)+x_(2)<=a
,x_(1)>=0,x_(2)>=0
,ainR
```

For which values of a does the LP have an alternative optimal solution(Draw the feasible region for one value)? For which values of

`a`

is the LP infeasible? For which values of a does the LP have a unique solution? Fix a specific value of a for which the feasible region is nonempty and the find the cone of exit, at each of the corner points. Fix a specific value of a such that the LP has alternative optimal solutions. Find the standard form LP. Using formulas construct the optimal table directly without any simplex iterations.