Abstract
Managing the distribution of limited resources to meet the needs of people has always been a global issue that faces managers, administrators, business owners, leaders of institution and individuals alike. With the increase in number of students admitted in Federal Polytechnic Nasarawa, with a large population of about 10,000, there would be undue stress on the facilities on campus. The class rooms are not sufficient or adequate and not well-assigned compared to the measurable number of students available. This has given rise to the reduction in the length of time a lecturer spends in class, distractions from students because of classroom proximity, amongst others. These cause extreme distress on the students and lecturers alike as they are unable to study or teach, respectively, to their highest potential as a result of resources or amenities that are inadequate or wanting. Data were collected from Federal Polytechnic Nasarawa Central Examination Committee for 2022/2023 Academic Session. The linear and integer programming methodology was employed. From the result of the linear programming (LP), seven (7) out of the seventy-eight (78) available classrooms has been fully utilized. The study revealed that if the remaining seventy-one (71) classrooms are fully utilized and maximized, they will improve the current objective function with a seating capacity of 4, 640. The result of the integer programming (IP) using the branch and bound method revealed that fourteen (14) out of the seventy-eight (78) available classrooms has been fully utilized. It asserted that if the remaining sixty-four (64) classrooms are fully utilized and maximized they will improve the current objective function with a seating capacity of 7,131. The result of the sensitivity analysis indicates that the entire classroom has an allowable increase thus validating the proposed models. The study therefore concludes that classroom space utilization is being underutilized leading to congestion and overflow in the utilized classrooms.

Key words: Linear Programming, Integer Programming, Allocation, classrooms.