The admission office at Tech wants to determine how many in-state and out-of state students to accept for next fall's entering freshman class. Tuition for in-state student is $7,600 per year while out-of- state tuition is $22,500 per year. A total of 12,800 in-state and 8,100 out-of-state freshman have applied for next fall, and Tech does not want to accept more than 3,500 students. However, since Tech is a state institution, the state mandates that it can accept no more than 40% out-of-state students. From past experience, the admissions office knows that 12% of in-state students and 24% of out-of-state students will drop out during their first year. Tech wants to maximize total tuition while limiting the total attrition to 600 first-year students.
- a) Formulate a linear programming model for this problem.
- b) Solve this model using the graphical method in order to find the optimal number of in-state and out-of-state students admitted.