Student Name: Stephen House
Competency 309.3.1: Decision-Making Models – The graduate uses optimizing models and other models as aids for making more informed decisions.
Graphical models enable a manager to visualize the objective function (profit line), constraints, and possible solutions to a given problem, and to make more informed decisions based on that information. In this task you will be using your knowledge of graphical models, the given scenario, and the attached “QAT1 Task 2 Spreadsheet” to complete the assessment.
Company A produces and sells a popular pet food product packaged under two brand names, with formulas that contain different proportions of the same ingredients. Company A made this decision so that their national branded product would be differentiated from the private label product. Some product is sold under the company’s nationally advertised brand (Brand Y), while the re-proportioned formula is packaged under a private label (Brand X) and is sold to chain stores. Because of volume discounts and other stipulations in the sales agreements, the contribution to profit from the Brand Y product sold to distributors under the company’s national brand is only $12.50 per case compared to $100 per case for private label product Brand X. There are four ingredients involved in the two products. The recipes specifying the use of each ingredient in the two product brands are given in the “QAT1 Task 2 Spreadsheet”. Also note that an ingredient may either be in limited supply or may have government regulations requiring a minimum or maximum amount.
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A. Identify the objective function.
1. Determine the total profit to be made if the company produces a combination of cases of Brand X and Brand Y that lies on the black-dashed objective function line (profit line), as shown on the graph in the attached “QAT1 Task 2 Spreadsheet.”
B. Write the four constraints that are described in the scenario given in the attached “QAT1 Task 2 Spreadsheet.”
1. Describe why each of the four written constraints from part B is a minimum or a maximum constraint.
C. Analyze the optimum production yielding the greatest amount of profit by doing the following:
1. Determine the number of cases of Brand X that should be produced, showing all of your work.
2. Determine the number of cases of Brand Y that should be produced, showing all of your work.
3. Discuss how the feasible region was used to arrive at your calculations for parts C1 and C2.
4. Determine the total profit that would be generated by the production levels determined in parts C1 and C2, showing all of your work.
Note: Partial cases are allowed as part of the solution.
D. When you use sources, include all in-text citations and references in APA format.
Note To reduce unnecessary matches select ignore “small matches <20 words” and “bibliography.”
Note: For definitions of terms commonly used in the rubric, see the Rubric Terms web link included in the Evaluation Procedures section.
Note: When using sources to support ideas and elements in an assessment, the submission MUST include APA formatted in-text citations with a corresponding reference list for any direct quotes or paraphrasing. It is not necessary to list sources that were consulted if they have not been quoted or paraphrased in the text of the assessment.
Note: No more than a combined total of 30% of a submission can be directly quoted or closely paraphrased from outside sources, even if cited correctly. For tips on using APA style, please refer to the APA Handout web link included in the APA Guidelines section.