Problem 4: (Cutting Stock and Column Generation) [20 points] Consider the following Cutting Stock problem with three orders: size 65 rolls, size 103 rolls, size 145 rolls. The ordered rolls have to be cut from larger rolls of size 26 . (a) (4 points) Formulate the IP problem that minimizes the the number of used roll of size 26, satisfying the orders. The decision variables should be the number of rolls of each size in each larger roll. (b) (4 points) Formulate the IP problem using the set covering formulation where the decision variables indicate which cutting patterns to use. (c) (4 points) Given initial cutting patterns: [5,0,0],[0,2,0],[0,0,1], formulate and solve the master problem with a solver or method of your choice, obtain the solution and the dual variables. (d) (4 points) Using the obtained dual variables, formulate and solve the subproblem with a solver or method of you choice and obtain a new pattern. (e) (4 points) Explain whether you can stop or continue the algorithm and what would be the stopping criteria