400 Question #3: Huron College is admitting students for the class of 2020. Data on its applicants are shown in the table below. GPA Score Business Majors Non-Business Majors In-Province 80 1500 In-Province 70 1300 700 In-Province 65 500 500 Out-of-Province 80 350 50 Out-of-Province 70 400 400 Out-of-Province 65 400 600 Huron College has set four goals for this class, listed in order of priority: Goal 1: The entering class should include at least 5000 students. Goal 2: The entering class should have an average GPA score of at least 74. Goal 3: The entering class should consist of at least 25% Out-of-Province students. Goal 4: At least 2000 members of the entering class should not be business majors. Use preemptive goal programming to determine how many applicants of each type to admit. Assume that all applicants who are admitted will decide to attend Huron. Formulate the goal programming model by defining your decision variables, objective function, and all relevant constraints. Solve the model using the Excel Solver to obtain the optimal solution. What is the optimal solution and the value of the objective function? MSCI-3200-1 Quantitative Decision Models II (No need to submit a spreadsheet). Hint: Define your decision variables as Xij = number of students admitted in each category. For example, category 1: In-Province business majors with 80 GPA; category 2: In-Province non-business majors with 80 GPA; category 3: In-Province business majors with 70 GPA, etc. Also, in writing some of the model constraints you may find the following example useful. A fruit basket contains 5 apples, 2 oranges and 3 pears. An apple weighs 95 grams, an orange 130 grams, and a pear 178 grams. What is the average weight of the fruit in the basket? Answer: (95) + 1(130) + (95) = 126.9 grams. 400 Question #3: Huron College is admitting students for the class of 2020. Data on its applicants are shown in the table below. GPA Score Business Majors Non-Business Majors In-Province 80 1500 In-Province 70 1300 700 In-Province 65 500 500 Out-of-Province 80 350 50 Out-of-Province 70 400 400 Out-of-Province 65 400 600 Huron College has set four goals for this class, listed in order of priority: Goal 1: The entering class should include at least 5000 students. Goal 2: The entering class should have an average GPA score of at least 74. Goal 3: The entering class should consist of at least 25% Out-of-Province students. Goal 4: At least 2000 members of the entering class should not be business majors. Use preemptive goal programming to determine how many applicants of each type to admit. Assume that all applicants who are admitted will decide to attend Huron. Formulate the goal programming model by defining your decision variables, objective function, and all relevant constraints. Solve the model using the Excel Solver to obtain the optimal solution. What is the optimal solution and the value of the objective function? MSCI-3200-1 Quantitative Decision Models II (No need to submit a spreadsheet). Hint: Define your decision variables as Xij = number of students admitted in each category. For example, category 1: In-Province business majors with 80 GPA; category 2: In-Province non-business majors with 80 GPA; category 3: In-Province business majors with 70 GPA, etc. Also, in writing some of the model constraints you may find the following example useful. A fruit basket contains 5 apples, 2 oranges and 3 pears. An apple weighs 95 grams, an orange 130 grams, and a pear 178 grams. What is the average weight of the fruit in the basket? Answer: (95) + 1(130) + (95) = 126.9 grams