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 the above question: provide a list of decision variables (2 points), objective function (2 points), and constraints (2 points), sketch the feasible region (2 points), and identify the optimal solution on the graph (2 points). 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.