1- Solve the following linear programming model by the Simplex Method to find the Optimal Solution :

Maximum ( Z ) = 6X1 + 10X2 --------------- (OF)

Subject to : X1 8 ----------(1)

4X2 24 ----------(2)

6X1 + 4X2 36 ----------(3)

X1 , X2 0

2- Consider the following linear programming problem, using the Simplex Big M method:

Minimum ( Z ) = 8X1 + 12X2 --------------- (OF)

Subject to : 2X1 + X2 10 ----------(1)

4X1 + 10X2 40 ----------(2)

4X1 + 5X2 = 20 ----------(3)

X1 , X2 0

1- Prepare the First Starting Table of Simplex

2- Is it an optimal solution or not? And why?

3- Determine the entering variable (EV) and leaving variable (LV), and the Pivot element.