Consider the following linear programming problem $(25$ pts$)$

Max $8x+7Y$

$s.t.3x+Y25$

$,5x+3Y30$

$,x+Y8$

$,x,Y0$

a$.$ Change to Standard Form;

b$.$ Use a graph to show each constraint and the feasible region.

c$.$ Identify the optimal solution point on your graph. What are the values of $x$ and $Y$ at the optimal solution?

d$.$ What is the optimal value of the objective function?