A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $40 on a Basic Set, $50 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers.

Required:

a. How many sets of each type should be made up and sold in order to maximize the profit?

b. What is the maximum profit?