Kevin Smith received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Kevin's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Kevin's task somewhat by adding the following stipulations:
homework can account for up to 25% of the grade, but must be at least 5% of the grade;
the project can account for up to 25% of the grade, but must be at least 5% of the grade;
the mid-term and final must each account for between 10% and 40% of the grade but cannot account for more than 70% of the grade when the percentages are combined; and
the project and final exam grades may not collectively constitute more than 50% of the grade.
a) Formulate an LP model that allows Kevin to maximize his numerical grade.
b) Create a spreadsheet model for this problem and solve it using Solver.
c) What is the optimal solution?
Use Solver to create a Sensitivity Report and answer the following questions:
d) Is there anything Kevin can request of his instructor to improve his final grade ?(Hint, for example he may ask the instructor to increase or/and decrease the weights of certain graded instruments)
e) Kevin has been approved by his instructor to increase the total weight allowed for the project and final exam by 5%. What will his new final grade score be?