qat1 tasks 1 5 495369

SUBDOMAIN 309.3 – QUANTITATIVE ANALYSIS Competency 309.3.1: Decision-Making Models – The graduate uses optimizing models and other models as aids for making more informed decisions. Objective 309.3.1-03: Interpret the solution depicted by a graphical linear programming model. Objective 309.3.1-11: Interpret the constraints depicted on a graphical linear programming model. Objective 309.3.1-12: Interpret the objective function depicted on a graphical linear programming model. Introduction: 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. Given: 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 X), while the re-proportioned formula is packaged under a private label (Brand Y) and is sold to chain stores. Because of volume discounts and other stipulations in the sales agreements, the contribution to profit is $40 per case for product sold to distributors under the company’s Brand X national brand compared to $30 per case for the Brand Y private label product. An ample supply is available of most of the pet food ingredients; however, three additives are in limited supply. The tight supply of nutrient C (one of several nutrient additives), a flavor additive, and a color additive all limit production of both Brand X and Brand Y. The formula for a case of Brand X calls for 4 units of nutrient C, 12 units of flavor additive, and 6 units of color additive. The Brand Y formula per case requires 4 units of nutrient C, 6 units of flavor additive, and 15 units of…