Problem $1.$

$(1$ 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.

min$2\mathrm{.}13Z_1+24\mathrm{.}24Z_2$

$s.t.$

$17\mathrm{.}61Z_1+3\mathrm{.}01Z_{2}39$

$9\mathrm{.}96Z_1+9\mathrm{.}08Z_{2}131$

$6\mathrm{.}8Z_1+4\mathrm{.}82Z_{2}38$

$17\mathrm{.}49Z_1+0\mathrm{.}68Z_{2}21$

$Z_1,Z_{2}0$

Optimal value:

Optimal solution:

Range of optimality for $Z_2$ :

Shadow price for constraint $3$:

Range of feasibility for constraint $3$ :

id: $1480$

Note: You can earn partial credit on this problem.