Class Component Weighting Problem
JJ is a business student. He has just completed a course in Business Analytics which had a midterm exam, a final exam, case studies, and recitation worksheets. He earned an 87% on the midterm exam, 96% on the final exam, 92% on the case studies, and 88% on recitation worksheets. The instructor is allowing his students to determine their own weights for each of the four grade components – of course, with some restrictions:
• The weight of the recitation worksheets score cannot be more than 15% of the total.
• The weight of the midterm exam score must count at least three times as much as the weight of the case study score.
• The weight of the final exam score must count at least twice as much as the weight of the case study score.
• The weights of each of the four components of the grade must be at least 10% of the course grade.
• The weights must sum to 100%.
Formulate as a linear program to maximize JJ’s grade in the class.
 

Goal Programming
K has decided to invest in off-campus student housing in a college in a town close to his retirement home in Central Florida. He will have to make 30% down payments on the apartment complexes since mortgage companies will only finance 70% of the purchase price of investment properties. The annual percentage rate is 5.75%. Monthly expenses (maintenance, insurance, and utilities) are estimated to 3% of the purchase price.
Florida laws require that each off-campus apartment houses only one student per bedroom. There is a strong demand for student housing, so we may assume that all of the apartments will be rented.
Apartment Type Monthly Rental per Student Monthly Rental per Apartment
One Bedroom $1,200 $1,200
Two Bedroom $1,000 $2,000
Three Bedroom $600 $1,800
There are 10 apartment complexes available. The pertinent information on each apartment complex is shown in the table below:

K has the following constraints that cannot be violated.
(1) The total monthly rent from the one-bedroom apartments cannot exceed 45% of the total monthly rent.
(2) The total monthly rent from the two-bedroom apartments cannot exceed 40% of the total monthly rent.
(3) The total monthly rent from the three-bedroom apartments cannot exceed 35% of the total monthly rent.
(4) The total number of apartments cannot exceed 120.
K initially ran a linear program with binary decision variables (1 for “Buy”, 0 for “Don’t Buy”) There was an optimal solution that would satisfy all of their constraints simultaneously with all decision variables for the apartment complexes being binary.