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  3. 3 a paper company sells rolls of paper of fixed...

Question: 3 a paper company sells rolls of paper of fixed...

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3. A paper company sells rolls of paper of fixed length in six standards widths: 6, 9, 12, 15, 20, and 24 feet. Its manufacturing process produces 30-foot-wide rolls only, so all orders must be cut from stock of this size. The demands for the 6, 9, 12, 15, 20, and 24-foot rolls are 130, 70, 48, 36, 15, and 20 rolls, respectively. The problem is to cut the 30-foot manufactured rolls in a fashion that minimizes the total number required. There are a variety of ways of cutting the standards widths from the 30-foot-wide rolls, three of which are shown below. Notice that some patterns result in wasted paper (shown in gray) that must be discarded. Pattern 1: No waste 6 9 Pattern 2: 1 waste 9 20 1 Pattern 3:3 waste 15 12 3 Other cutting patterns are possibl... To somewhat simplify the situation, do not include patterns that have a waste as great as the smallet standard width (6 feet). Also assume that each roll can be cut only in one pattern. a) Clearly define the ALL the cutting patterns (how many are there?) and the decision variables. b) Write the appropriate LP model to minimize the total number of 30-foot rolls required to satisfy the demands. c) Solve the LP model using Excel. Clearly explain the optimal solution.
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