Exercises: Solve the following problems by the Simplex Algorithm.
1) Max z = 2 X1 + 4 X2 + 5 X3 + 3 X4
s.t.
2 X1 - X2 + 2 X3
≤ 10
X1 + 2 X2
+ 2 X4 ≤ 20
X1, X2, X3, X4 ≥ 0
Solution: z = 90, x1=0, x2=10, x3=10, x4=0, x5=0, x6=0
2) Min z = 2 X1 - 4 X2 + 5 X3 - 3 X4
s.t.
2 X1 - X2 + 2 X3
≤ 10
X1 + 2 X2
+ 2 X4 ≤ 20
X1, X2, X3, X4 ≥ 0
Solution: z = -40, x1=0, x2=10, x3=0, x4=0, x5=20, x6=0
3) Min z = 2 X1 - 4 X2 - 5 X3
s.t.
2 X1 - X2 + 2 X3 ≤ 40
X1 + 2 X2
≤ 10
X2 + 3 X3 ≤ 20
X1, X2, X3 ≥ 0
Solution: z = -45, x1=0, x2=5, x3=5, x4=35, x5=0, x6=0
4) Max z = 2 X1 + 3 X2 - 5 X3
s.t.
2 X1 - X2 + 2 X3 ≤ 40
X1 + 2 X2
≤ 10
X2 + 3 X3 ≤ 20
X1, X2, X3 ≥ 0
Solution: z = 20, x1=10, x2=0, x3=0, x4=20, x5=0, x6=20
5) Max z = 2 X1 + 3 X2 + 6 X3
s.t.
2 X1 X1
X2 + 2 X3 ≤ 40
≤ 10
-2 X2 + 3 X3 ≤ 20
X1, X2, X3 ≥ 0
Solution: Unbounded