11. Choosing an Assortment. National Metals Company (NMC) manufactures titanium shafts. Its equipment is capable of producing shafts in ten lengths, reecting different settings on its machinery. These lengths are 32 to 50 cm in steps of 2 cm. Setting up the machinery to produce one of these lengths (which is done once a week) costs $250. As a result, NMC has decided to make only a selected number of lengths. When a customer requests a given length, NMC may supply it from stock if it happens to match one of the lengths in the production schedule. Otherwise, NMC trims a longer length to meet the order. The variable cost for producing the shafts is $20 per cm, and NMC receives revenue of $40 per cm. Trim waste can be sold to a recycler for $15 per cm. The demand requirements for the coming week are tabu- lated as followsall demand must be satised: Length 32 34 36 38 40 42 44 46 48 50 (cm) Demand 12 4 7 8 16 7 12 5 8 3 What is an optimal assortment of lengths for NMC to manufacture