Much of the QNBRC business is carrying fuel from the refineries in Montr$$al and

distributing it to other cities in Eastern Canada. QNRBC carries three types of fuel:

crude oil, gasoline, and liquefied natural gas $($LNG$).$ As a shipping manager, you

have to determine the cargo that one of the trains will contain.

Each railway car full of crude oil weighs $4$ thousand tonnes, requires $5$ labour$-$hours

of handling, and generates $$10$ thousand in profits.

Each car full of gasoline weights $2$ thousand tonnes, requires $5$ labour$-$hours of

handling, and generates $$8$ thousand in profits.

Finally, each car full of LNG weighs $4$ thousand tonnes, requires $10$ labour$-$hours of

handling, and generates $$15$ thousand in profits.

If the length of the train cannot exceed $100$ railway cars, the weight of the train

cannot exceed $300$ thousand tonnes, and a maximum of $650$ labour$-$hours are

available for handling, how many cars of each kind of fuel should the train contain

in order to maximize profits?