Suppose that P1, P2, and P3 are variables whose values are 1 if a particular plant is to be opened and 0 otherwise. Write a single linear constrain that reflect each of the following four cases

(a) if plant 1 is opened, then plant 2 must also be opened

(b) Not more than two of the three plants should be opened

(c) if neither Plant 2 nor Plant 3 is opened, then Plant 1 should not be opened

(d) if plant 1 is opened or plant 3 is not opened then plant 2 must be opened