Linear Programming Techniques and Its Application in Optimizing Lecture Room in an Institution

This paper deals with linear programming techniques and their application in optimizing lecture rooms in an institution. This linear programming formulated based on the available secondary data obtained from the information Technology units of an institution as the secondary data as well as the primary data source obtained by the researchers, which includes measuring the classroom dimension, lecture current seating capacity, number of registered students in each of department within the eight (8) schools in the institution, number of registered students per programme in each department in the schools totaling 3249. Maximizing the current available classroom space using AMPL software revealed that in all the available 32 lecture rooms with a current seating capacity of 2023 to accommodate a total student population of 3249, the finding revealed three (3) important solutions, which were categorized as: 1) For the calculated current good seating capacity can accommodate 9234 students and 2) the calculated current seating capacity of both good and bad seating can accommodate 10,431 students and 3) the projected seating capacity as indicated by the AMPL software can accommodate 13,300 students with current and existing 32 lecture rooms for all departments in the eight (8) schools provided that the seating capacities is fully maximize and this will help the school management to have more internal revenue.as school fees using the same and current classroom facility assuming each students pays GH？1500.00 as academic fees yearly, the institution could generate an additional GH？ 8977, 500.00 in revenue for the good sitting capacity only if it is fully maximized, i.e. (5985 × GHc1500.00); GHc.10,773,000.00 (7182 × GH？1500) for the current sitting capacity, and GHc.15,076,500.00 as internal revenue, i.e. (10,051 students × GH？1500.00) from the projected seating capacity respectively while maintaining the same lecture room and seating capacity were fully maximized.