# Quantitative Analysis

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SUBDOMAIN 309.3 – QUANTITATIVE ANALYSIS

Competency 309.3.1: Decision-Making Models –

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 from the Brand Y private label product is only \$30 per case compared to \$40 per case for product sold to distributors under the company’s Brand X national brand.

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 color additive. The supply of the three ingredients for each production period is limited to 30 units of nutrient C, 72 units of flavor additive, and 90 units of color additive.

A. Determine the equations for each of the three constraints that are plotted on the attached “Graph 1,” showing all work necessary to arrive at the equations.

1. Identify each constraint as a minimum or a maximum constraint.

B. Determine the total contribution to profit if the company produces a combination of cases of Brand X and Brand Y that lies on the purple objective function (profit line) as it is plotted on the attached “Graph 1.”

C. Determine how many cases each of Brand X and of Brand Y you recommend should be produced during each production period for optimum production if Company A wants to generate the greatest amount of profit, showing all of your work.

D. Determine the total contribution to profit that would be generated by the production level you recommend in part C, showing all of your work.

E. When you use sources, include all in-text citations and references in APA format.

Page 1 of 1

## QAT1 Task 309.3.1-03, 11, 12

Not applicable.

Not applicable.

Not applicable.

Not applicable.

Not applicable.

Levels/Criteria

Unacceptable

Needs Revision

Meets Standard

Exemplary

Score/Level
Articulation of Response (clarity, organization, word usage, ease of understandability)

There is no evidence of response to the prompts.

The articulation of the response is weak.

The articulation of the response is adequate.

The articulation of the response is skillful.

Accuracy of Mechanics (grammar, punctuation, spelling)

The work includes several major errors that disrupt the meaning or flow of the response.

The work includes a few major errors and/or many minor errors that interfere with the clarity of the response.

The work includes a few minor errors but no readily detectable major errors.

The work includes no readily detectable major or minor errors.

A. Equations

The candidate correctly determines the equation for 0–1 constraints that are plotted on the graph.

The candidate correctly determines the equation for 2 constraints that are plotted on the graph.

Not applicable.

The candidate correctly determines the equation for 3 constraints that are plotted on the graph.

A1. Minimum or Maximum Constraint

The candidate correctly identifies 0–1 constraints as minimum or maximum constraints.

The candidate correctly identifies 2 constraints as minimum or maximum constraints.

The candidate correctly identifies 3 constraints as minimum or maximum constraints.

B. Total Contribution of Profit

The candidate does not correctly determine the total contribution to profit if the company produces a combination of cases of Brand X and Brand Y that lies on the purple objective function (profit line) as it is plotted on the attached “Graph 1.”

The candidate correctly determines the total contribution to profit if the company produces a combination of cases of Brand X and Brand Y that lies on the purple objective function (profit line) as it is plotted on the attached “Graph 1.”

C. Optimum Production

The candidate does not correctly determine how many cases of each brand should be produced during each production period for the greatest amount of profit, or does not show all work.

The candidate does not correctly determine how many cases of each brand should be produced during each production period for the greatest amount of profit, but shows all work.

The candidate correctly determines how many cases of each brand should be produced during each production period for the greatest amount of profit, showing all work.

D. Total Contribution to Profit

The candidate does not correctly determine the total contribution to profit generated by recommended production level from part C, or does not show all work.

The candidate does not correctly determine the total contribution to profit generated by recommended production level from part C, but shows all work.

The candidate correctly determines the total contribution to profit generated by recommended production level from part C, showing all work.

E. Sources

When the candidate uses sources, the candidate does not provide in-text citations and/or references for each source used.

When the candidate uses sources, the candidate provides appropriate in-text citations and/or references with major deviations from APA style.

When the candidate uses sources, the candidate provides appropriate in-text citations and/or references with minor deviations from APA style.

When the candidate uses sources, the candidate provides appropriate in-text citations and/or references with no readily detectable deviations from APA style, OR the candidate does not use sources.

Overall Holistic

Unacceptable

Needs Revision

Meets Standard

Exemplary

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