. Suppose that you are interested in choosing a set of investments {1, . . . , 7}. Assume that the investments have cost of $5, $7, $6, $3, $9, $12, $5. Assume there is a budget of $30. Also assume that the eventual expected prot out of each investment is $1, $3, $2, $4, $1, $5, $4. Write an optimization model to maximize prot with the following constraints. The objective function and all the constraints should be linear and there may be integer variables. Dene all variables you need and explain the constraints that you write down. (a) You must choose at least one of the investments. (b) Investment 1 cannot be chosen if investment 3 is chosen. (c) Investment 4 can be chosen only if investment 2 is also chosen. (d) You must choose either both investments 1 and 5 or neither. (e) You must choose either at least one of the investments 1, 2, 3 or at least two investment from 2, 4, 5, 6