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

Answer:

b. X1 + X2 ≤ X3 + X4

Explanation:

b. X1 + X2 ≤ X3 + X4

The situation tells us that the sum of both 1 and 2 must be equal to the sum of 3 and 4 which is true, because if both projects 1& 2 are selected then the both projects 3 & 4 must also be selected.

The rest of the choices are wrong because

a. X1 + X2 ≤ 2(X3 + X4)

The sum of projects 1& 2  is not less than 2 times sum of projects 3 & 4 .

c. X1 − X3 = X2 − X4

If we leave project 3 then project 4 cannot be left out.

d. X1 + X2 + X3 + X4 ≤ 2

any two projects out of the four cannot be chosen. 1 must be chosen from 1&2  and the other from 3 &4.