Professor Wang teaches two sections of operations management, which combined will result in 130 final exams to be graded. Professor Wang has two graduate assistants (GAs), James and Ann, who will grade the final exam. There is a 3-day period between the time the exam is administered and when final grades must be posted. During this period James has 14 hours available and Ann has 12 available hours to grade the exams. It takes James an average of 8.4 minutes to grade an exam, and it takes Sarah 15 minutes to grade an exam; however, James’s exams will have errors that will require Professor Wang to ultimately regrade 12% of his exams, while only 5% of Ann’s exams will require regrading. Professor Wang wants to know how many exams to assign to each GA to grade in order to get all of them graded, but she also wants to minimize the number of exams that she will be required to regrade.
a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.
c. Solve this model using Excel.
d. If Professor Wang could hire James or Ann to work one more hour, which should she choose? What would be the effect of hiring the selected GA for one additional hour?