Conceptual Overview: Explore how linear programming constraints establish the feasible region.

Par, Inc. manufactures both standard and deluxe golf bags. Processes including (a) cutting and dyeing, (b) sewing, (c) finishing, and (d) inspection and packaging constrain the relative numbers of the two kinds of bags that can be produced. For example, Par, Inc. has the resources for cutting and dyeing to make (7/10)th Standard bags for every Deluxe bag up to a total of 630. That is, (7/10)S + 1D <= 630 is one constraint of their manufacturing process. This and the other constraints are listed below.

Initially, the graph below shows the unconstrained choices for the number of Standard and Deluxe bags to be made. Click on the graph to apply each constraint in order; each constraint applied is highlighted. Note that some constraints reduce the feasible alternative combinations of Standard and Deluxe substantially, while other constraints are laxer and reduce the feasible set little or not at all. Click on the graph, noting the changes with each new constraint, until all the constraints have been applied. The remaining highlighted area is the feasible set.

(7/10)S + 1D <= 630 Cutting and Dyeing

(1/2)S + (5/6)D <= 600 Sewing

1S + (2/3)D <= 708 Finishing

(1/10)S + (1/4)D <= 135 Inspection and Packaging

1. Which constraint results in a least upper bound for the optimal number of Deluxe Bags? __________

1. Cutting & Dyeing
2. Sewing
3. Finishing
4. Inspection & Packaging

2. Which constraint results in a least upper bound for the optimal number of Standard Bags? __________

1. Cutting & Dyeing
2. Sewing
3. Finishing
4. Inspection & Packaging

3. Which constraint could be removed without affecting the feasible solution region? ___________

1. Cutting & Dyeing
2. Sewing
3. Finishing
4. Inspection & Packaging