Professor Smith teaches two sections of business statistics, which combined will result in 120 final exams to be graded. Professor Smith has two graduate assistants, Brad and Sarah, who will grade the final exams. There is a 3-day period between the time the exam is administered and when final grades must be posted. During this period Brad has 12 hours available and Sarah has 10 hours available to grade the exams. It takes Brad an average of 7.2 minutes to grade an exam, and it takes Sarah 12 minutes to grade an exam; however, Brad’s exams will have errors that will require Professor Smith to ultimately regrade 10% of the exams, while only 6% of Sarah’s exams will require regrading. Professor Smith wants to know how many exams to assign to each graduate assistant to grade in order to minimize the number of exams to regrade.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.