Consider this linear program:

Minimize $,Z=27x+67y$

Subject to $\frac{1}{6}x+\frac{1}{4}y1,(C_1)$

$6x+\frac{7}{2}y21,(C_2)$

$x\frac{11}{2},(C_3)$

$\frac{1}{7}y1,(C_4)$

$x,y0$

$($a$)$ Graph the feasible region for the constraints. $(50\%)$

Drawing the feasible region requires $3$ mouse clicks for each

constraint. Use the first two clicks to draw the line and the third

click to select the region satisfying the constraint.

Draw: $($b$)$ Graph only the feasible region.

$(10\%)$

Click once on each corner point of the feasible region to draw it$.$

Then click on the first point again to close and shade it$.$

Draw: $($c$)$ State the optimal solution point and the objective function value. $(30\%)$

Enter your answers below as fractions or decimals accurate to at least

$4$ decimal places. Do not use rounded values to calculate the objective

function value. Use exact values.

The optimal solution occurs at

$x=$

$,y=$

The optimal objective function value, $Z=$

$($d$)$ At optimal solution, which constraints are non$-$binding? $(10\%)$

Select all that apply.

$C_1$

$C_2$

$C_3$

$C_4$