Consider a scheduling model in which a machine can be switched on at most k times during a horizon of T periods. In this model, there are two sets of variables: yt = 1 if the machine is on during period t, and zt = 1 if the machine is switched on in period t. Then the constraints look like the following: X T t=1 zt k zt yt + yt1 0, t = 1, . . . , T zt yt , t = 1, . . . , T yt , zt {0, 1}, t = 1, . . . , T where y0 is taken to be zero in the second set of constraints. Show that the constraint matrix is TU.