Determine the objective functions, constrains (without forgetting the non negativity) showing the mathematical equations.

A shipline company requires a fleet of ships to serve requirement for carrying cargo between six cities. There are four specific routes that must be served daily. These routes and the number of ships required for each route are as follows Route # Origin Destination Number of Ships per Day Needed Dhahran New York 3 1 2 Marseilles Istanbul 2 1 4 3 Naples Bombay New York Marseilles All cargo are compatible, and only one type of ship is needed. The travel time matrix between cities is shown, it Naples Marseilles Istanbul N York Dhahran Bombay Naples 2 14 7 7 Marseilles 0 3 13 8 8 1 IE 0906701 Advanced Operations Research 1 Istanbul 2 3 0 15 5 5 Days t; matrix New York 14 13 15 0 17 20 Dhahran 7 8 5 17 0 3 Bombay 7 8 5 20 3 0 Takes one day to off-load and one day to on-load each ship. How many ships must the shipline company purchase. (Hint: ships coming off of some route get assigned to some other routes, each route gets its required number of ships per day) Route # 1 2 3 4 Origin Dhahran Marseilles Naples New York Destination New York Istanbul Bombay Marseilles Number of Ships per Day Needed 3 2 1 1 Naples Marseilles Istanbul N York Dhahran Bombay Naples 0 1 2 14 7 7 Marseilles 1 0 3 13 8 8 Istanbul 2 3 0 15 5 5 New York 14 13 15 0 17 20 Dhahran 7 8 5 17 0 3 Bombay 7 8 5 20 3 0 the number of ships per day coming off route i and assign to routej Days t; matrix bi: represent the number of ships per day required on route I cy: on loading + days for transit on route i + off loading + days for travel from the destination of route i to the origin of routej C11= 1 +17+1 +17 = 36 A shipline company requires a fleet of ships to serve requirement for carrying cargo between six cities. There are four specific routes that must be served daily. These routes and the number of ships required for each route are as follows Route # Origin Destination Number of Ships per Day Needed Dhahran New York 3 1 2 Marseilles Istanbul 2 1 4 3 Naples Bombay New York Marseilles All cargo are compatible, and only one type of ship is needed. The travel time matrix between cities is shown, it Naples Marseilles Istanbul N York Dhahran Bombay Naples 2 14 7 7 Marseilles 0 3 13 8 8 1 IE 0906701 Advanced Operations Research 1 Istanbul 2 3 0 15 5 5 Days t; matrix New York 14 13 15 0 17 20 Dhahran 7 8 5 17 0 3 Bombay 7 8 5 20 3 0 Takes one day to off-load and one day to on-load each ship. How many ships must the shipline company purchase. (Hint: ships coming off of some route get assigned to some other routes, each route gets its required number of ships per day) Route # 1 2 3 4 Origin Dhahran Marseilles Naples New York Destination New York Istanbul Bombay Marseilles Number of Ships per Day Needed 3 2 1 1 Naples Marseilles Istanbul N York Dhahran Bombay Naples 0 1 2 14 7 7 Marseilles 1 0 3 13 8 8 Istanbul 2 3 0 15 5 5 New York 14 13 15 0 17 20 Dhahran 7 8 5 17 0 3 Bombay 7 8 5 20 3 0 the number of ships per day coming off route i and assign to routej Days t; matrix bi: represent the number of ships per day required on route I cy: on loading + days for transit on route i + off loading + days for travel from the destination of route i to the origin of routej C11= 1 +17+1 +17 = 36