$(x,Y).$ 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.

min$7\mathrm{.}37x_1+19\mathrm{.}71x_2$

$s.t.$

$13\mathrm{.}88x_1+0\mathrm{.}84x_{2}21$

$11\mathrm{.}41x_1+25\mathrm{.}53x_{2}157$

$x_1,x_{2}0$

Optimal value:

Optimal solution:

Range of optimality for $x_2$ :

Shadow price for constraint $2$:

Range of feasibility for constraint $2$ :$(1$ 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$)$:

$1.$ Use square brackets when the endpoint is included $($all values except infinity$)$

$2.$ Use parenthesis when the endpoint is $*$not$*$ included.

$3.$ 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.