3. Suppose that you are interested in choosing a set of investments {1,,7} using 0 1 variables. Model the following constraints using only linear equations (obs: operators such as or or if can not be used): (a) You cannot invest in all of them. (b) You must choose at least one of them. (c) Investment 1 cannot be chosen if investment 3 is chosen. (d) Investment 4 can be chosen only if investment 2 is also chosen. (e) (bonus) You must choose either both investments 1 and 5 or neither. (f) (bonus) You must choose either at least one of the investments 1,2,3, or at least two investments from 2,4,5,6.