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

Paper Company plant produces rolls of paper of various types forits customers. One product type is rolls of wrapping paper inseveral different standard widths, as follow: 12, 15, 20, 24, 30,or 40 inches. The various-width rolls are produced by slicing60-inch wide rolls in plant. For a given week, company waits forall its customer orders to come in and then decides how to sliceits 60-inch rolls to satisfy that week’s orders, to minimize thewaste (i.e., the part of the rolls sliced that’s not used forcustomers’ orders that week). [For example if customer orders in aparticular week totaled six 15-inch wide rolls and two 40-inch widerolls, the orders could be satisfied by appropriately slicing three60-inch wide rolls, leaving only two 5-inch waste rolls.]

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

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