Question 1 Merlion LuxBus Pte Ltd provides point-to-point coach services between Singapore and various Cities in Malaysia. It competes based on differentiated luxury and on-time services. It owns a fleet of 12 buses, each with a capacity of only 24 passengers in a 2 is to 1 seating arrangement per row and up to 8 rows. This allows the seats to be nearly fully reclined with good leg room for passengers. Singapore is the hub of Merlion's operations. Point-to-point travel service means that buses will depart in the morning for a Malaysian city. The same buses will return to Singapore with Malaysian passengers in the evening. The COVID 19 pandemic in 2020 and 2021 closed land travel between Singapore and Malaysia. This severely affected the business of Merlion. To cope with the downturn, they pivoted towards local tour services. With both countries now moving towards the endemic phase of COVID19 and opening up quarantine-free cross border travel, Merlion is now planning to revert to its core business of luxury point-to-point services between the 2 countries. Table 1. Daily Market Demand (passengers) From \\ To Singapore Malacca Kuala Lumpur Penang Singapore 0 200 350 120 Malacca 250 Kuala Lumpur 400 Penang 100 Table 1 shows the projected daily demand for its services at each city. For example, there are some 350 daily customers who want to take its coach service from Singapore to Kuala Lumpur. Similarly, there are some 400 daily customers who want to take its service from Kuala Lumpur back to Singapore. There is no direct service between Malaysian cities. Table 2. Profit Per Passenger ($) From \\ To Singapore Malacca Kuala Lumpur Penang Singapore 0 15 30 33 Malacca 15 0 0 Kuala Lumpur 30 0 0 Penang 33 Table 2 shows the profit per passenger per ride between Singapore and each Malaysian city and vice versa. Merlion needs to plan how to deploy its fleet of buses to cover each route so that it can maximise its profit.Using the given information, demonstrate how you would apply the Linear Programming Technique to help Merlion plan its bus deployment. (a) State three (3) practical assumptions applicable to this particular linear programming (LP) problem. (6 marks) (b) Develop an LP model to maximise daily profit for Merlion. Your model must be in the form of algebraic equations and inequalities all of which must be annotated. Define your Decision Variables, Objective Function and Constraints clearly. (14 marks)