Consider the following linear programming problem

Max	8X + 7Y
s.t.	15X + 5Y 75
	10X + 6Y 60
	X + Y 8
	X, Y 0

a.	List all the extreme points of the feasible region.
b.	Find the optimal solution and the objective function value.
c.	List the values of all the slack variables.

A: a. (0,0), (5,0), (3.75,3.75), (4,6), (0,8); b. x=4, y=6, OFV=74; c. s₁=0 , s₂=0 , s₃=2.

B:a. (0,0), (5,0), (3.75,3.75), (3.5,4.5), (0,8); b. x=3.5, y=4.5, OFV=59.5; c. s₁=0 , s₂=2 , s₃=0.

C:a. (0,0), (5,0), (3.5,4.5), (0,8); b. x=3.5, y=4.5, OFV=59.5; c. s₁=0 , s₂=2 , s₃=0.

D:a. (0,0), (5,0), (8,0), (3.5,4.5), (0,8), (0,10) ; b. x=0, y=10, OFV=70; c. s₁=25 , s₂=0 , s₃=2.

E:a. (0,0), (5,0), (3.75,3.75), (3,4), (0,8); b. x=3.75, y=3.75, OFV=56.25; c. s₁=0 , s₂=0 , s₃=0.5.

F:a. (0,0), (5,0), (3.75,3.75), (3,5), (0,8); b. x=3, y=5, OFV=59; c. s₁=5 , s₂=0 , s₃=0.

G:a. (0,0), (5,0), (8,0), (3.5,4.5), (0,8) ; b. x=8, y=0, OFV=64; c. s₁=45 , s₂=20 , s₃=0.

H:a. (0,0), (3,0), (3.75,3.75), (3,5), (0,4); b. x=3, y=5, OFV=59; c. s₁=5 , s₂=0 , s₃=0.

I:a. (0,0), (5,0), (8,0), (3.5,4.5), (0,8), (0,15) ; b. x=0, y=15, OFV=105; c. s₁=0 , s₂=30 , s₃=7.

J:a. (0,0), (5,0), (3.75,3.75), (6,4), (0,8); b. x=6, y=4, OFV=76; c. s₁=5 , s₂=0 , s₃=2.