A bakery employs a skilled pastry chef, who should work at least 6 hours per day. An oven suitable for the use of the chef is available 8 hours per day. Three types of pastry are to be made; each batch requires labor time (in hours) by the chef and time in the oven as below:

Suppose that the profit per batch is \(\$ 10\) for type \(1, \$ 5\) for type 2 , and \(\$ 10\) for type 3 pastry. How many batches of each pastry type should be made to maximize profit?

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Chef time: Pastry type 1 2 3 112 Oven time: 2 1 2