please answer all the parts (a, b, c) without using a solver

Problem 2: (LP formulation) [20 points) AE-AIR flies from Abu Dhabi to Jeddah, Amman, Muscat, and Kuwait. It has three different types of aircraft's. The following table presents the capacity of each aircraft type and number of aircraft's for each type. 1 4 1600 Aircraft Type Capacity (passenger) Number of Aircraft's 1 50 15 2 30 12 3 20 20 Number of passengers per day flying to each city is given in the table below. The table also shows the number of trips that each aircraft can make to the four cities. Aircraft Type Number of daily trips per route Jeddah Amman - Muscat Kuwait 3 2 2 1 2 4 3 32 5 2 Daily number of customers 2000 900 1200 The operating costs for flying one aircraft of a type to a destination and penalty cost of losing one passenger to other airlines are given in the table below. Aircraft Type Operating Cost per Round Trip on Route (1000 AED) Jeddah Amman Muscat Kuwait 20 11 2 10 8 8 Penalty per lost passenger (AED) AF-AIR has to decide the number of aircraft's of each type to be assigned to each route so as to minimize the total operating and penalty costs. Hint. Here is a sample assignment: Aircraft Assigned Aircraft's Assigned Available Type Jeddah Amman Muscat Kuwait Aircraft's Aircrafts 6 15 15 2 12 12 3 4 20 In the above assignment, daily number of passengers flying to Jeddah is equal to 16 Typel) * (3 Trips) * (50 capacity) + (2 Type2) * (4 Trips) * (30 capacity) + (4 Type3) * (5 Trips) * (20 capacity) = 1540 That means 1600 - 1540 - 60 passengers to Jeddah will be lost to other airlines 1 12 9 16 12 15 10 9 3 4 5 7 6 1 2 1 4 2 4 2 4 16 Answer the following questions: (a) (4 points) Write down the decision variables for this problem. (b) (6 points) Write down the objective function of this problem. (c) (10 points) Write down the constraints. Problem 2: (LP formulation) [20 points) AE-AIR flies from Abu Dhabi to Jeddah, Amman, Muscat, and Kuwait. It has three different types of aircraft's. The following table presents the capacity of each aircraft type and number of aircraft's for each type. 1 4 1600 Aircraft Type Capacity (passenger) Number of Aircraft's 1 50 15 2 30 12 3 20 20 Number of passengers per day flying to each city is given in the table below. The table also shows the number of trips that each aircraft can make to the four cities. Aircraft Type Number of daily trips per route Jeddah Amman - Muscat Kuwait 3 2 2 1 2 4 3 32 5 2 Daily number of customers 2000 900 1200 The operating costs for flying one aircraft of a type to a destination and penalty cost of losing one passenger to other airlines are given in the table below. Aircraft Type Operating Cost per Round Trip on Route (1000 AED) Jeddah Amman Muscat Kuwait 20 11 2 10 8 8 Penalty per lost passenger (AED) AF-AIR has to decide the number of aircraft's of each type to be assigned to each route so as to minimize the total operating and penalty costs. Hint. Here is a sample assignment: Aircraft Assigned Aircraft's Assigned Available Type Jeddah Amman Muscat Kuwait Aircraft's Aircrafts 6 15 15 2 12 12 3 4 20 In the above assignment, daily number of passengers flying to Jeddah is equal to 16 Typel) * (3 Trips) * (50 capacity) + (2 Type2) * (4 Trips) * (30 capacity) + (4 Type3) * (5 Trips) * (20 capacity) = 1540 That means 1600 - 1540 - 60 passengers to Jeddah will be lost to other airlines 1 12 9 16 12 15 10 9 3 4 5 7 6 1 2 1 4 2 4 2 4 16 Answer the following questions: (a) (4 points) Write down the decision variables for this problem. (b) (6 points) Write down the objective function of this problem. (c) (10 points) Write down the constraints