# Assume a large number of cardboard sheets with 23 inch

Assume a large number of cardboard sheets with 23 inch width is available. From these 23 inch sheets, we need to cut sheets with width 6 inch and 8 inch, in only one direction. The demand for sheets with width 6 inch is 3000, while the demand for sheets with width 8 inch is 2000. Suppose:

–We lose 5¢ by wasting every inch of a sheet,

–We incurred the cost of 1¢ for storing every extra 6” sheet,

–We incurred the cost of 3¢ for storing every extra 8” sheet.

We would like to minimize the loss, while satisfying the demand.

Formulate the optimization model for this question: provide a list of decision variables, objective function, and constraints, sketch the feasible region, and identify the optimal solution __on the graph__. Hint: the objective function consists of two terms: (1) cost of wastage (2) cost of storage. Writing the first term is quite straightforward. For writing the second term, you may need to use your constraints; in fact, subtracting the right-hand side of the constraints (i.e. demand) from the left-hand side of the constraints (i.e. number of sheets (with width 6 inch or 8 inch) being cut) gives you the extra sheet being cut.