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.
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.