Question

Let X1 and X2 be 0 - 1 variable whose values indicate whether projects 1 and 2 are not done or are done.
Which answer below indicates that project 2 can be done only if project 1 is done?

• A. X1 - X2 ≥ 0
• B. X1 + X2 = 2
• C. X1 + X2 = 1
• D. X1 - X2 ≤ 0

Answer 1

solution:

given that data Let X1 and X2 be 0 - 1 variable whose values indicate whether projects 1 and 2 are not done or are done.
Which answer below indicates that project 2 can be done only if project 1 is

So

since x1, x2 are binary variables they take values 0 or 1

if you take for not done and 1 for done

x1+x2 =1 does not ensure x2=1

x+x2 =2 iff x1=x2=1 both are done

x1-x2<=0 is possible if x1=0 or 1 and x2 can be 0 hencce it does not ensure x2=1

x1-x2>=0 also does not ensure x2=1 , it is possible both zero or x1=1

hence x1+x2=2 ensures that project 2 can be done only if project 1 is done