1. A paper company has two cutting machines. One cuts raws of length 100 and the other cuts raws of length 200. The cost of a cutting pattern depends on the cutting machine. For the 100-long raws, the cost of a pattern is $5. For the 200-long raws, the cost of a pattern is $10. The objective is to meet the orders of Table 1 at a minimum cost Table 1: Orders characteristics Length of final Quantity 20 2.000 30 1,500 40 1.000 Due to quality restrictions, the only patterns allowed for the 100-long raws are: 5 finals of length 20 3 finals of length 30 2 finals of length 40. For the 200-long raws, the only patterns allowed are: 10 finals of length 20 6 finals of length 30 5 finals of length 40. 1. Formulate the problem of fulfilling the orders at a minimum cost. 2. Give the dual LP. 3. Obtain an initial set of basic variables for this model. Give the corresponding plan, i.e. the BFS, and its cost, i.e. objective function value. 4. Perform one iteration of the Revised Simplex algorithm. 5. Give the new plan and its cost. Is it optimal? 1. Find an initial set of basic variables 2. Solve the system Bb' = b 3. Solve the system yB = CB 4. If yN Cj 6. Solve the system Bd = a; 7. If d 0} dk HINT 1. A paper company has two cutting machines. One cuts raws of length 100 and the other cuts raws of length 200. The cost of a cutting pattern depends on the cutting machine. For the 100-long raws, the cost of a pattern is $5. For the 200-long raws, the cost of a pattern is $10. The objective is to meet the orders of Table 1 at a minimum cost Table 1: Orders characteristics Length of final Quantity 20 2.000 30 1,500 40 1.000 Due to quality restrictions, the only patterns allowed for the 100-long raws are: 5 finals of length 20 3 finals of length 30 2 finals of length 40. For the 200-long raws, the only patterns allowed are: 10 finals of length 20 6 finals of length 30 5 finals of length 40. 1. Formulate the problem of fulfilling the orders at a minimum cost. 2. Give the dual LP. 3. Obtain an initial set of basic variables for this model. Give the corresponding plan, i.e. the BFS, and its cost, i.e. objective function value. 4. Perform one iteration of the Revised Simplex algorithm. 5. Give the new plan and its cost. Is it optimal? 1. Find an initial set of basic variables 2. Solve the system Bb' = b 3. Solve the system yB = CB 4. If yN Cj 6. Solve the system Bd = a; 7. If d 0} dk HINT