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variables and constraints in this problem

Edmonds Paper Products manufactures a variety of products for commercial applications. In one of its processes, rolls of 100 inch wide paper are cut into smaller-width rolls of the same length. Orders for different width rolls are received at various times each week. Current economic conditions have forced Edmonds to abandon the prior practice of meeting demand on a short-time turnaround basis using machine operator estimates which have resulted in excessive waste. For Edmonds , waste is defined as both trim loss and surplus. Trim loss is defined as the leftover portion of a 100 inch roll after cutting to meet specific size requirements. Surplus waste is generated when more rolls of a specific width are cut than are demanded. Machine operators, intending to minimize the number of cuts per roll by creating an inventory of common sizes, have increased logistical costs as well as inventory costs for the company. Edmonds has implemented a policy to complete all orders on a weekly basis to meet demand and minimize waste. This week, the company has orders for 30, 50, 25, and 90 rolls of 60, 48, 36, and 24 inch widths respectively. Edmonds needs to determine all possible ways to cut these widths from 100 inch rolls and to minimize trim and surplus waste.
a. Formulate a linear programming model that can be used to determine the optimal product width type mix that yields the minimum total contribution to trim and surplus waste while meeting the individual product and weekly production requirements for Edmonds Paper Products, Inc .


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Please see attached files. I have two tabs created in the excel file. One is Integer ...

Solution Summary

The solution studies the variables and constraints in this problem. These linear programming problems are clearly broken down.