Use appropriate big-M values wherever needed. (a) Use binary variables xt for t = 1, . . . , T to denote whether we have a transaction in period t (xt = 1) or not (xt = 0). Write down a linear constraint to enforce that if we have a transaction in the first period than we can have transactions in at most half of the remaining periods. You can assume T is an odd number. Justify your formulation. (b) xi for i = 1, 2, 3 are continuous nonnegative variables with values in the range [0, 3]. Write a set of constraints to model the requirement that: |2x1 x2 x3|2 by introducing an additional binary variable. Justify your formula- tion. (c) x1 and x2 are integer variables whose values are restricted to be in [0, 10]. Write a set of constraints to model the requirement that: eitherx1+x2 10or2x1x2 5butnotboth by introducing an additional binary variable. 2. In Radiation therapy for cancer, beams of radiation are directed at can- cerous tissue from various positions. The goal is to find the intensity of the radiation beams at each position so that the deposited radiation dose on cancer cells exceed required levels