#$4)$ Solve the following LP

Maximize $$5$x $+$ $$6$y

Subject to $2$x $+3$y $<=10($labor$,$ in hours$)$

$6$x $+6$y $<=36($materials$,$ in pounds$)$

$7$x $+5$y $<=40($storage$,$ in square feet$)$

x$,$ y $>=0$

a$)$ Write the original optimal solution and objective function value.

b$)$ What is the optimal solution and objective function value if you acquire $2$ additional pounds of material?

c$)$ What is the optimal solution and objective function value if you acquire $1\mathrm{.}5$ additional hours of labor?

d$)$ What is the optimal solution and objective function value if you give up $1$ hour of labor and get $1\mathrm{.}5$ pounds of material?

e$)$ What is the optimal solution and objective function value if you introduce a new product that has a profit contribution of $$2?$ Each unit of this product will use $1$ hour of labor, $1$ pound of material, and $2$ square feet of storage space.