A shoe manufacturer produces mid-top and high-top athletics shoes. Cutting machines cut the fabric for the shoes. Stitching machines stitch the fabric. The cutting machines run 4 hours per day, and the stitching machines run 5 hours per day. A mid-top shoe takes 1 minute to cut, and 2 minutes to stitch. A high-top shoe takes 3 minutes to cut, and 2 minutes to stitch. The profit is $13 on a mid-top shoe and $16 on a high-top shoe. Determine how many shoes of each kind should be made in order to maximize profits, and what the maximum possible profit is.
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