Problem 1. (40 points) A company has to be split in two children companies, called sub-company A and sub-company B. The mother company sells three products throughout 7 branches all over the world; the revenue of each branch from the selling of each product is reported in the table in Fig. 1. Each branch can be assigned either to sub-company A or sub-company B (but not to both). Part I (20 points): a) (12 points): Formulate a linear program that finds the optimal way to distribute the 7 branches across the two sub-companies in order to minimize the maximum difference (in absolute value) between the revenue of sub-company A and that of sub-company B, for each of the 3 products. b) (8 points): Solve the LP using Matlab (or any other solver at your choice). Provide i) the optimal solution; ii) the optimal objective value; and iii) the Matlab script used to solve the problem. Part II (20 points): a) (12 points): Change now the formulation with the goal of minimizing the difference in absolute value) of the total revenue between the two sub-companies; b) (8 points): Solve the LP using Matlab (or any other solver at your choice). Provide i) the optimal solution; ii) the optimal objective value; and iii) the Matlab script used to solve the problem. Branch CON Products 1 2 3 83 14 42 38 63 56 28 24 12 597 53 25 35 83 52 86 85 5964 25 O Figure 1: Table for Problem 1