Using the simplex Method Maximize z 4x 2y subject to x y

Using the simplex Method

Maximize z = 4x + 2y

            subject to

                                    x - y < 10

                                    5x + 3y < 75

                                    x + y < 20

                                                x > 0

                                                y > 0

Solution

Maximize z = 4x + 2y

subject to

x-y<10
5x+3y<75
x+y<20

Table #1
==========================================================
x y s1 s2 s3 z   
==========================================================
1 -1 1 0 0 0 10   
5 3 0 1 0 0 75   
1 1 0 0 1 0 20   
-4 -2 0 0 0 1 0

Table #2
==========================================================
x y s1 s2 s3 z   
==========================================================
1 -1 1 0 0 0 10   
0 8 -5 1 0 0 25   
0 2 -1 0 1 0 10   
0 -6 4 0 0 1 40   

Table #3
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x y s1 s2 s3 z   
==========================================================
1 0 3/8 1/8 0 0 105/8
0 1 -5/8 1/8 0 0 25/8   
0 0 1/4 -1/4 1 0 15/4   
0 0 1/4 3/4 0 1 235/4

Optimal Solution: z = 235/4; x = 105/8, y = 25/8