Explain how the following conditions can be represented as linear constraints using binary variables.

a. Either x1 + x2 ≤ 3 or 3x1 + 4x2 ≥ 10

b. Variable x2 can assume values 0, 4, 7, 10 and 12 only

c. If x2 ≤ 3, then x3 ≤ 6; otherwise, x3 ≤ 4 (assume x2 and x3 are integers)

d. At least two out of the following five constraints must be satisfied:

x1 + x2 ≤ 7 x1 – x2 ≥ 3 2x1 + 3x2 ≤ 20 4x1 – 3x2 ≥ 10 x2 ≤ 6 x1, x2 ≥ 0