Question

If a company selects either of Project 1 or Project 2 (or both), then either Project 3 or Project 4 (or both) must also be selected. Which of the following constraints enforce this condition?

a. X1 + X2 ≤ 2(X3 + X4)

b. X1 + X2 ≤ X3 + X4

c. X1 − X3 = X2 − X4

d. X1 + X2 + X3 + X4 ≤ 2

Answer 1

Select - Option - A ......... X₁+ X₂ ≤ 2(X₃ + X₄)

Explanation.

The company select project - 1 only when Project - 3 and Project - 4 are individually or collectively better than or equal to it.

Hence ............. X₁ ≤ (X₃ + X₄)

The company select project - 2 only when Project - 3 and Project - 4 are individually or collectively better than or equal to it.

Hence ............. X₂ ≤ (X₃ + X₄)

Now X1 or X2 or Both implies .............

X₁ + X₂ = (X₃ + X₄) + (X₃ + X₄)

X₁ + X₂ = 2X₃ + 2X₄

X₁ + X₂ = 2(X₃ +X₄)