Use the Simplex method to find the maximum optimal solution

Use the Simplex method to find the maximum optimal solution for the following problems: Please show all steps including the optimization model, the Simplex Table, all row operations to solving the simplex table, and graphing the solution. Maximize z = 5a + 3b + c

Subject to: a + b + c <= 6

5a + 3b + 6c <= 15

a,b,c >= 0

Solution

Maximise p = 5x + 3y + z

x + y + z 6

5x + 3y + 6z 15

x 0

y 0

z 0

Table #1
==========================================================
x y z s1 s2 s3 s4 s5 p   
==========================================================
1 1 1 1 0 0 0 0 0 6
5 3 6 0 1 0 0 0 0 15   
1 0 0 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-5 -3 -1 0 0 0 0 0 1 0

Table #2
==========================================================
x y z s1 s2 s3 s4 s5 p   
==========================================================
1 1 1 1 0 0 0 0 0 6
5 3 6 0 1 0 0 0 0 15   
-1 0 0 0 0 1 0 0 0 0
0 1 0 0 0 0 -1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-5 -3 -1 0 0 0 0 0 1 0

Table #3
==========================================================
x y z s1 s2 s3 s4 s5 p   
==========================================================
1 1 1 1 0 0 0 0 0 6
5 3 6 0 1 0 0 0 0 15   
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 -1 0 0
-5 -3 -1 0 0 0 0 0 1 0

Table #4
==========================================================
x y z s1 s2 s3 s4 s5 p   
==========================================================
1 1 1 1 0 0 0 0 0 6
5 3 6 0 1 0 0 0 0 15   
-1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
-5 -3 -1 0 0 0 0 0 1 0

Table #5
==========================================================
x y z s1 s2 s3 s4 s5 p   
==========================================================
0 0.4 -0.2 1 -0.2 0 0 0 0 3
1 0.6 1.2 0 0.2 0 0 0 0 3
0 0.6 1.2 0 0.2 1 0 0 0 3
0 -1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 1 0 0
0 0 5 0 1 0 0 0 1 15   

Optimal Solution occurs on x = 3 , y = 0 and z = 0 , p = 15