A small factory produces two types of toys: trucks and bicycles. In the manufacturing process two machines are used: the piece maker and the assembler. It takes 2 hours to make the pieces of the bicycles and 1 hour for the trucks. To assemble the pieces, it takes 2 hours for the bicycles and 3 hours for the trucks. The piece maker can be operated for 16 hours a day and there are two assemblers which can each be used for 12 hours a day. Each bicycle gives a profit of $16 and each truck gives a profit of $14. Formulate and solve a linear programming problem so that the factory maximizes its profit.