Korey is a business student at State U. She has just completed a course in decision models, which had a midterm exam, a final exam, individual assignments, and class participation. She earned an 86% on the midterm, 94% on the final, 93% on the individual assignments, and 85% on participation. The benevolent instructor is allowing his students to determine their own weights for each of the four grade components; of course, with some restrictions:
- The participation grade can be no more than 15% of the total.
- The midterm grade must count at least twice as much as the individual assignment score.
- The final exam grade must count at least three times as much as the individual assignment score.
- Each of the four components must count for at least 10% of the course grade.
- The weights must sum to 1.0 and be nonnegative.
a. Develop a model that will yield a valid set of weights to maximize Korey's score for the course.
b. Implement your model on a spreadsheet and find a good solution using only your intuition.
c. Find an optimal solution using Solver.