4. Recall the cutting stock problem from Lecture 2. A paper company produces paper rolls with a standard width of 21 feet each. Customer orders with different widths are produced by cutting the standard rolls into different widths. The company currently uses the following knife settings. Setting A: 5ft+7ft+9ft Setting B: 5ft+5ft+7ft+ 4ft Setting C: 5ft+5ft+9ft +2ft Setting D: 9ft+9ft +3ft Currently, there is a demand of 150 for 5ft rolls, and 210 for 7 ft rolls and 280 for 9 ft rolls. Using a formulation similar to what we developed in class we have the following linear program: Decision variables: i: The number of standard rolls to be cut using setting i: i= A,B,C,D Min A+B+C+D s.t. A+ 2B +2C > 150 (5ft roll) A + B > 210 (7ft roll) A + C +2D > 280 (9 ft roll) A, B, C, D > 0

a) Solve this model using Excel Solver or AMPL and generate sensitivity report. Provide screen shots.

b) The company is considering several different new knife settings. Evaluate the introduction of each option by itself i. Setting E: 5ft+5ft+5ft+5ft+1ft Use the sensitivity report to justify if this settings should be introduced. Show your work and explain. (hint: price out the new setting. Note that this is a minimization problem) ii. Setting F: 7ft + 7ft + 7 ft Use the sensitivity report to justify if this settings should be introduced. Show your work and explain. (hint: price out the new setting. Note that this is a minimization problem)