Problem $2.$

$(1$ point$)$ Solve the linear program below using graphical methods $($either the extreme point or iso$-$profit line methods$).$ When entering your answers, specify the "optimal solution$*$ as a 'point", i$.$e$.$ enter coordinates X and Y as

$(x,Y).$ When entering a range $($i$.$e$.$ range of optimality or range of feasibility$)$:

Use square brackets when the endpoint is included $($all values except infinity$)$

Use parenthesis when the endpoint is "not" included.

Use $-$inf and inf to represent values of minus infinity and infinity respectively.

For example, if the lower endpoint is $5$ and the upper endpoint is $7\mathrm{.}25,$ you would enter $[5,7\mathrm{.}25].$ If the lower endpoint is minus infinity and the upper endpoint is $1\mathrm{.}65,$ you would enter $(-$inf, $1\mathrm{.}65].$

If the linear program cannot be solved, specify one of the following for the optimal value and specify $0$ for all other answers:

$1-$ Solution is suboptimal

$2-$ Empty feasible region

$3-$ Unbounded feasible region

$4-$ All other reasons

Enter all values to two decimal places.

max$5\mathrm{.}87x_1+12\mathrm{.}12x_2$

$s.t.$

$13\mathrm{.}46x_1+6\mathrm{.}13x_{2}171$

$12\mathrm{.}86x_1+9\mathrm{.}26x_{2}158$

$x_1,x_{2}0$

Optimal value:

Optimal solution:

Range of optimality for $x_1$ :

Shadow price for constraint $2$:

Range of feasibility for constraint $2$:

id: $1490$

Note: You can earn partial credit on this problem.