Estimate a range for the optimal objective value for the following LPs:

(a) Minimize z = 5x1 + 2x2

Subject to

X1 - x2 ≥ 3

2x1 + 3x2 ≥ 5

X1, x2 ≥ 0

(b) Maximize z = x1 + 5x2 + 3x3

Subject to

X1 + 2x2 + x3 = 3

2x1 - x2 = 4

X1, x2, x3 ≥ 0

(c) Maximize z 2x1 + x2

Subject to

X1 - x2 ≤ 10

2x1 ≤ 40

X1, x2 ≥ 0

(d) Maximize z = 3x1 + 2x2

Subject to

2x1 + x2 ≤ 3

3x1 + 4x2 ≤ 12

X1, x2 ≥ 0