436 BUSINESS ANALYTICS MODULE BLINEARPROGRAMMINGBUSINESSANAL YTICSMODULELinear ProgrammingDISCUSSIONQUESTIONS1.Students may select from eight LP applications given in the introduction: school bus scheduling, police patrol allocation, schedulingbank tellers, selecting product mix, picking blends to minimize cost, minimizing shipping cost, developing production schedules, andallocating space.LO B.1:Formulate linear programming models, including an objective function and constraints AACSB:Reflective thinking2.LP theory states that the optimum lies on a corner. All three solution techniques make use of the “corner point” feature.LO B.3:Graphically solve an LP problem with the corner-point method AACSB:Reflective thinking3.The feasible regionis the area bounded by the set of problem constraints. A feasible solutionis any combination of x, ycoordinates (orx1, x2 coordinates) that is in or on the feasible region.LO B.2:Graphically solve an LP problem with the iso-profit line method AACSB:Reflective thinking4.Each LP problem that has been formulated correctly doeshave an infinite number of possible solutions. Any point within the feasibleregion is a solution that satisfies all constraints (although it is not necessarily optimal). In addition, for any problem in which the optimalsolution lies on a constraint that is parallel to the objective function, all points along that constraint are also both feasible andoptimal.LO B.2:Graphically solve an LP problem with the iso-profit line method AACSB:Reflective thinking5.The objective function contains the profit or cost information that enables us to determine whether one solution is better than an-othersolution. Our choice of best depends onlyon the objective.LO B.1:Formulate linear programming models, including an objective function and constraints AACSB:Reflective thinking6.Before activity values can be placed into the objective, they must meet the constraints. Notice that the objective function has nominimum-required profit level unless it is included as a constraint.LO B.1:Formulate linear programming models, including an objective function and constraints AACSB:Reflective thinking7.As long as the costs do not change, the diet problem always provides the same answer. In other words, the diet is the sameevery day.Unlike animals, people enjoy variety, and variety cannot be included as a linear constraint.
437 BUSINESS ANALYTICS MODULE BLINEARPROGRAMMINGLO B.6:Formulate production-mix, diet, and labor scheduling problems AACSB:Reflective thinking8.The number of feasible solutions is infinite. We only need to consider extreme points—corner points—to find the optimal solution. Ifwe use iso-profit lines, we only need to examine one corner point to determine the optimal solution.