Poly Products sells packaging tape to industrial customers. All tape is sold in 100-foot rolls that are cut in various widths from a master roll, which is 15 inches wide. The product line consists of the following widths: 2", 3", 5", 7", and 11". These can be cut in different combinations. For example, one combination might consist of three cuts of 5" each. Another combination might consist of two 2" cuts and an 11" cut. Both of these configurations use the entire 15-inch roll without any waste, but other configurations are also possible. For example, another combination might consist of two 7" cuts. This combination creates 1 inch of waste for every roll cut this way. Each week, Poly Products collects demands from its customers and distributors and must figure out how to configure the cuts in the master rolls. To do so, the production manager lists all possible combinations of cuts and tries to fit them together so that waste is minimized while demand is met. (In particular, demand must be met exactly, because Poly Products does not keep inventories of its tape.) This week's demands are shown in the following table:

a. How many configurations can be cut from a 15-inch master roll so that there is less than 2 inches of waste (i.e., the smallest quantity that can be sold) left on the roll?
b. What is the minimum amount of waste that can be created if all demand is met exactly?

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Size Demand 3" 5" 40 2" 11" 20 7" 50 30 60