$(5)$ Consider the following linear programming model with $4$ regular constraints:

Maximize $6x+10Y$

subject $to$: $2x+1Y20(constraint\frac{?}{?}$#$1)$

$4x+4Y48(constraint\frac{?}{?}$#$2)$

$4x+3Y50(constraint\frac{?}{?}$#$3)$

$x2(constraint\frac{?}{?}$#$4)$

$x,Y0(non-$negativity constraints$)$

$($a$)$ Draw your graph in the space below:

$($a$)$ Which of the constraints is redundant? Constraint #

Justify by drawing a graph like Figure $7\mathrm{.}14$ on p$.263$

$($b$)$ Is point $(9,3)$ a feasible solution?

Justify by analyzing the following constraints.

Constraint #$1$:

Constraint #$2$:

Constraint #$3$

Constrsing #$4$

$($c$)$ Which of the following points yields the best solution? Underline the best solution: $(7,5),(9,2),(6,6).$

Justify your answer $($using the data from the above LP model$).$

$(7,5)$:

$(9,2)$:

$(6,6)$: