Reference no: EM132241708

For the following provide (a) algebraic formulation, (b) optimized model using Excel-Solver, and (c) statement of the optimal solution.

Paper Company plant produces rolls of paper of various types for its customers. One product type is rolls of wrapping paper in several different standard widths, as follow: 12, 15, 20, 24, 30, or 40 inches. The various-width rolls are produced by slicing 60-inch wide rolls in plant. For a given week, company waits for all its customer orders to come in and then decides how to slice its 60-inch rolls to satisfy that week’s orders, to minimize the waste (i.e., the part of the rolls sliced that’s not used for customers’ orders that week). [For example if customer orders in a particular week totaled six 15-inch wide rolls and two 40-inch wide rolls, the orders could be satisfied by appropriately slicing three 60-inch wide rolls, leaving only two 5-inch waste rolls.]

company wants to use the minimum number of 60-inch rolls to meet each week’s customer orders, minimizing waste – with waste being defined as any part of rolls that is not being shipped out to meet that week’s customer orders for which rolls were sliced.

company needs to determine how many 60-inch rolls are to be used to meet this week’s customer orders, totaling 48 12-inch wide rolls, 19 15-inch wide rolls, 22 20-inch wide rolls, 32 24-inch wide rolls, 14 30-inch wide rolls, and seven 40-inch wide rolls.