Problem 4: Goal Programming (35 points) Major Bill Bligh, director of the Army War Colleges new six-month attach training program, is concerned about how the 20 officers taking the course spend their precious time while in his charge. Major Bligh recognizes that there are 168 hours per week and thinks his students have been using them rather inefficiently. Bligh lets X1 = number of hours of sleep needed per week X2 = number of personal hours per week (eating, personal hygiene, handling laundry, and so on) X3 = number of hours of class and studying per week X4 = number of hours of social time off base per week (dating, sports, family visits, and so on) He thinks that students should go to class and study exactly 30 hours a week to have time to absorb materials. This is the most important goal. Bligh feels that students need at most 7 hours of sleep per night on average and that this goal is number 2 in term of priority. He believes that goal number 3 (least important goal) is to provide at least 20 hours per week of social time. a. Formulate this as a preemptive goal programming problem. Define the decision variables, objective function, and constraints. (20 points) b. Formulate this same problem on a spreadsheet and SOLVE using Excel solver (Provide the corresponding Excel Spreadsheet and the Answer Report). (11 points) c. Describe clearly and completely the solution to this problem using a managerial statement. (4 points)