Question: QUESTION # 2: MATHEMATICAL MODELLING (20 POINTS) (CLO 1).: Capital Development Authority (CDA) of Islamabad is studying the feasibility of introducing a transit bus system

QUESTION # 2: MATHEMATICAL MODELLING (20 POINTS)

QUESTION # 2: MATHEMATICAL MODELLING (20 POINTS) (CLO 1).: Capital Development Authority (CDA) of Islamabad is studying the feasibility of introducing a transit bus system that will alleviate the traffic and pollution problem by reducing in-city driving. The study seeks the minimum number of buses that can handle the transportation needs of Islamabad. After gathering necessary information, the city engineer noticed that the minimum number of buses needed fluctuated with the time of the day and that the required number of buses could be approximated by constant values over successive 4-hour intervals. The following figure summarizes the engineer's findings. To carry out the required daily maintenance, each bus can operate & successive hours a day only. Formulate (Only formulate) a linear programming model to determine the number of operating buses in each shift that will meet the minimum demand while minimizing the total number of buses in operation. 8 12 12 10 8 00 Number of buses 7 4 4 12.00 AM 4:00 8:00 12:00 Noon 4:00 8:00 12:00 Midnight

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