Problem 2. (25 points + 10 pts Bonus) A company in paper industry produces paper rolls with a standard width of 30-feet each. Special customer orders with different widths are produced by cutting (slitting) the standard rolls. Suppose at a given point in time, there is a need for 590 6-ft wide rolls, 380 8-ft wide rolls, and 650 11.ft wide rolls. Assuming a standard roll is of length L, and any extra (surplus) 6-ft, 8-ft, or 11.ft widths produced in excess of requirements must be thrown away, along with the end waste (trim loss), please answer the following: (a) Identify all logical cutting patterns (knife settings) as a table. (b) Formulate a Linear Programming model that will yield an optimal plan for the company to meet the demand with the least loss area of paper (due to inevitable trim loss and extra production) Before writing the model you should define your decision variables (assume them as continuous variables) and clearly express the loss area, (C) (Bonus) Reduce the objective function you developed above to an equivalent but simpler one. Explain how it is done. Problem 2. (25 points + 10 pts Bonus) A company in paper industry produces paper rolls with a standard width of 30-feet each. Special customer orders with different widths are produced by cutting (slitting) the standard rolls. Suppose at a given point in time, there is a need for 590 6-ft wide rolls, 380 8-ft wide rolls, and 650 11.ft wide rolls. Assuming a standard roll is of length L, and any extra (surplus) 6-ft, 8-ft, or 11.ft widths produced in excess of requirements must be thrown away, along with the end waste (trim loss), please answer the following: (a) Identify all logical cutting patterns (knife settings) as a table. (b) Formulate a Linear Programming model that will yield an optimal plan for the company to meet the demand with the least loss area of paper (due to inevitable trim loss and extra production) Before writing the model you should define your decision variables (assume them as continuous variables) and clearly express the loss area, (C) (Bonus) Reduce the objective function you developed above to an equivalent but simpler one. Explain how it is done