One-dimensional cutting stock problem: Lumber is supplied to a medium-sized furniture workshop in standard lengths of 100in. Different designs call for pieces of specified lengths that do not exceed 100in. 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?

*please use excel solver*