Introduction:
Graphical models enable a manager to visualize the objectivefunction (profit line), constraints, and possible solutions to agiven problem, and to make more informed decisions based on thatinformation.
Given:
Company A produces and sells a popular pet food product packagedunder two brand names, with formulas that contain differentproportions of the same ingredients. Company A made this decisionso that their national branded product would be differentiated fromthe private label product. Some product is sold under the company’snationally advertised brand (Brand X), while the re-proportionedformula is packaged under a private label (Brand Y) and is sold tochain stores.
Because of volume discounts and other stipulations in the salesagreements, the contribution to profit from the Brand Y privatelabel product is only $30 per case compared to $40 per case forproduct sold to distributors under the company’s Brand X nationalbrand.
An ample supply is available of most of the pet food ingredients;however, three additives are in limited supply. The tight supply ofnutrient C (one of several nutrient additives), a flavor additive,and a color additive all limit production of both Brand X and BrandY.
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. TheBrand Y formula per case requires 4 units of nutrient C, 6 units offlavor additive, and 15 units of color additive. The supply of thethree ingredients for each production period is limited to 30 unitsof nutrient C, 72 units of flavor additive, and 90 units of coloradditive.
Task:
A. Determine the equations for each of the three constraints thatare plotted on the attached “Graph 1,” showing all work necessaryto arrive at the equations.
1. Identify each constraint as a minimum or a maximumconstraint.
B. Determine the total contribution to profit if the companyproduces a combination of cases of Brand X and Brand Y that lies onthe purple objective function (profit line) as it is plotted on theattached “Graph 1.”
C. Determine how many cases each of Brand X and of Brand Y yourecommend should be produced during each production period foroptimum production if Company A wants to generate the greatestamount of profit, showing all of your work.
D. Determine the total contribution to profit that would begenerated by the production level you recommend in part C, showingall of your work.
ScholarMatic: Explanation & Answer
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