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6.10 One-Dimensional Cutting Stock Problem: Lumber is supplied to a medium- sized furniture workshop in standard lengths of 100 in. Different designs call for pieces of specified lengths that do not exceed 100 in. Nevertheless, the shop wants to use a minimum number of standard-length master pieces to accommodate a given list of required pieces. Today's list is shown in the table below. Design 1 2 3 4 5 6 7 8 9 10 11 Length 33 14 63 84 39 94 54 41 50 71 56 (a) Develop a rule of thumb to solve this problem. How many standard-length pieces are needed, using your rule of thumb? (b) What is the optimal solution? How close did your rule of thumb in (a) come to the optimum