Cory is an undergraduate student who just finished a course in linear programming. The course grade is composed of the following components:

midterm exam score, final exam score, individual assignments score and class participation score. Cory just received their final exam score; so, they know their percentage score on each of the four components of the course grade. Cory earned 86%

on the midterm exam, 94% on the final exam, 93% on the individual assignments and 82% on class participation. The default weights for the components are 0.25 each.

Hence, Cory’s total score is 0.25(86) + 0.25(94) + 0.25(93) + 0.25(82) = 88.75. The total score of 88.75 is a grade of B. A score of 90 and higher will earn an A for the course. Cory’s instructor has decided to allow the students to either take their default total score or try to maximize their total score, subject to the following restrictions:

● The participation score weight can be no more than 0.25.

● The midterm exam score weight must be at least twice as much as the participation weight.

● The final exam score weight must be at least three times as much as the participation weight.

● The weight for each of the four components must be at least 0.10.

● The weights used for each component must be nonnegative and the four weights must sum to one.

Cory has decided to try to maximize their grade.

a. Develop a linear programming model that could be used to maximize Cory’s total score.

b. Build and solve a spreadsheet model of the formulation from part (a). What are the optimal weights and what is Cory’s total score?

c. How much did the model improve Cory’s total score. Does Cory’s maximized score result in a better course letter grade? Explain.