Question: The vice president for marketing of the Super Grain Corporation
The vice president for marketing of the Super Grain Corporation needs to develop a promotional campaign for the company’s new breakfast cereal. Three advertising media have been chosen for the campaign, but decisions now need to be made regarding how much of each medium should be used. Constraints include a limited advertising budget, a limited planning budget, and a limited number of TV commercial spots available, as well as requirements for effectively reaching two special target audiences (young children and parents of young children) and for making full use of a rebate program. The corresponding linear programming model requires more than two decision variables, so a software package such as described in Sec. 3.5 or Sec. 3.6 will be needed to solve the model. This case also asks for an analysis of how well the four assumptions of linear programming are satisfied for this problem. Does linear programming actually provide a reasonable basis for managerial decision making in this situation?
Answer to relevant QuestionsUse the graphical method to solve the problem: Maximize Z = 10x1 + 20x2, Subject to and x1 ≥ 0, x2 ≥ 0, Reconsider the model in Prob. 4.1-4. (a) Introduce slack variables in order to write the functional constraints in augmented form. Consider the following problem. Maximize Z = 5x1 + 3x2 + 4x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Consider the following problem. Maximize Z = 2x1 + 4x2 + 3x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. (a) Work through the simplex method step by step in algebraic form. (b) Work through the simplex method step by step ...A basic property of any linear programming problem with a bounded feasible region is that every feasible solution can be expressed as a convex combination of the CPF solutions (perhaps in more than one way). Similarly, for ...
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