takes 3 4 hour to cut the leather for a sandal and 1 2 hour to cut the leather for a shoe. It takes 2 hours to sew the sandal together, and 1 hour to sew the shoe. It takes 2 hours to attach the soles onto a pair of sandals, and 1 hour to attach the soles onto a pair of shoes. A profit of $30 is made on each pair of sandals, and a profit of $40 is  made on each pair of shoes. If the staff is limited to 16 hours for cutting, 24 hours for sewing, and 12 hours for attaching soles, calculate the number of pairs of sandals and shoes they should produce to maximize profit.

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