A designer of expensive leather jackets created two new jacket designs for the new season: a long one and a short one. Each short leather jacket requires 1 labor hour from the cutting department and 3 labor hours from the sewing department. Each long leather jacket requires 2 labor hours from the cutting department and 4 labor hours from the sewing department. This designer is sharing cutting and sewing services with other designers, and as such, there are only 32 labor hours per week available in the cutting department and 84 labor hours per week available in the sewing department for him. In addition, because of the limited appeal of the long jacket, the distributor cannot take any more than 12 long jackets per week. If the designer makes $50 profit on each short leather jacket and $80 on each long one, how many of each type of jacket should he have manufactured per week to maximize his profits?