Suppose that x and y are binary variables whose values indic

Suppose that x, and y are binary variables whose values indicate whether projects are done or not done. Which constraint ensures that project 2 can be done only if project 1 is done?

x + y = 1

x + y = 2

x - y 0

x - y 0

Solution

since x, y are binary variables they take values 0 or 1

if you take for not done and 1 for done

x+y =1 does not ensure y=1

x+y =2 iff x=y=1 both are done

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

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

hence x+y=2 ensures that project 2 can be done only if project 1 is done