We have three 01 variables x1 x2 and x3 In the final solutio

We have three 0-1 variables: x1, x2 and x3. In the final solution, we wish to have no more than two of these variables be non-zero. On the other hand, we want at least one of them to be non-zero. Also, x3 cannot be non-zero unless x1 is non-zero. Write the constraints needed to accomplish this.
a. x1 + x2 +x3 <= 2, x1 - x3 =>0
b. x1 + x2 +x3 = 2, x3 - x1 => 0
c. x1 + x2 +x3 => 1, x1 + x2 = 1
d. x1 + x2 +x3 <= 3, x3 - 1 = 0
e. none of these

Solution

x1,x2,x3 out of these not more than 2 non zero. That means only at the most two can be non zero.

Also x3 cannot be non zero unless x1 is non zero. Hence either x1, x3 are non zero or x3 is non zero.

c. x1 + x2 +x3 => 1, x1 + x2 = 1 is right optin