Data Corp.is considering which of 4 different projects to undertake in order to maximize its net present value (NPV).Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4.The NPV and required capital (in millions)for each project are listed below.
Which of the following represents the constraint stating that project 3 can be undertaken only if project 2 is undertaken?
A)X2 + X3 ≤ 1
B)X2 - X3 ≤ 0
C)X3 - X2 ≤ 0
D)X2 - X3 ≤ 1
E)X3 - X2 ≤ 1

Question

Data Corp.is considering which of 4 different projects to undertake in order to maximize its net present value (NPV).Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4.The NPV and required capital (in millions)for each project are listed below.
 Which of the following represents the constraint stating that project 3 can be undertaken only if project 2 is undertaken?
A)X2 + X3 ≤ 1 
B)X2 - X3 ≤ 0 
C)X3 - X2 ≤ 0 
D)X2 - X3 ≤ 1 
E)X3 - X2 ≤ 1

Quizplus · Accepted Answer

If project 3 can be undertaken only if project 2 is undertaken, it means that X3 is dependent on X2. In other words, if X2 is 0, then X3 must also be 0. Therefore, the correct constraint would be X3 ≤ X2, which can be rewritten as X3 - X2 ≤ 0. Thus, the correct answer is (C).

Data Corpis Considering Which of 4 Different Projects to Undertake in in Order