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# An airline is investigati

An airline is investigating the possibility of reducing the cost of fuel purchases by taking advantage of lower fuel prices in certain airports. Fuel cost represents a substantial portion of operating expenses for an airline and thus, it is important that fuel purchases are carefully monitored. However, fuel adds weight to an airplane and consequently, excess fuel raises the cost of getting from one city to another.There are 4 cities: L, M, A and B. Considering 1 flight route in which a plane departs from L, flies from L to M, from M to A, A to B and from B to L. When the plane arrives in L, the flight circular route is said to be completed, and then it starts a new flight again. Thus, the amount of fuel on board in L must be taken into consideration when the flight circular route begins. Along each leg of this route, there is a minimum and a maximum amount of fuel that can be carried This input data is provided below:Leg ; Min fuel required; max fuel required; regular fuel consumption; fuel price per gallonL to M;24000;36000;12000;3.95M to A;15000;23000;7000;4.25A to B: 9000;17000;3000;4.10B to L: 11000;20000;5000;4.18The regular fuel consumption is calculated for a plane carrying the minimum amount of fuel. If more than the minimum is carried, the amount of fuel consumed is higher, i.e. for each 1000 gallons of fuel above the minimum, 5% of fuel is considered ?lost? due to excess fuel consumption. For example, if 25000 gallons of fuel were on board when the plane took off from L, the fuel consumed on this route would be 12000+50 = 12050, and if 26000 gallons of fuel were on board from L, then fuel consumed would be 12100 gallons etc.Assume that the airplaine starts the circular route from L with 15000 gallons on board. The task is to determine the optimal fuel purchase plan for a circular route at each city so as to minimise the fuel cost.Formulate the fuel purchase problem as a Linear Programming (LP) problem.*Please solve this question elaborately and quickly. Thanks! (Y)