A company produces three types of athletic shirt. A dozen tank tops requires 1 hour on the cutting machine, 2 hours on the sewing machine, and 3...

A company produces three types of athletic shirt. A dozen tank tops requires 1 hour on the cutting machine, 2 hours on the sewing machine, and 3 hours on the packaging machine. A dozen short-sleeve shirts requires 3 hours on the cutting machine, 5 hours on the sewing machine, and 5 hours on the packaging machine. A dozen long-sleeve shirts requires 6 hours on the cutting machine, 6 hours on the sewing machine, and 8 hours on the packaging machine. In one week, the cutting machine has a maximum of 21 hours that can be dedicated to these shirts, the sewing machine has a maximum of 28 hours that can be dedicated to these shirts, and the packaging machine has a maximum of 35 hours that can be dedicated to these shirts. How many dozen of each shirt can this company produce in one week assuming that the machines are used to maximum capacity?