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QAT1 Task 2 QUANTITATIVE ANALYSIS & Decision-Making Models

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Accounting

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Homework

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Task 309.3.1-03, 11, 12
Western Governors University
Task 2: QUANTITATIVE ANALYSIS & Decision-Making Models
X Y
Flavor 6 12
Nutrient 7.5 7.5
Color 15 6
The maximum allowable for each of the parts of the equation are listed as: Nutrient = 56.25 Units,
Flavor= 72 Units and Color= 90 Units.

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Number of units of N used must be less than or equal to 56.25 units
Number of units of F used must be less than or equal to 72 units
Number of units of C used must be less than or equal to 90 units
Variables:
X = Number of units of brand X
Y = Number of units of brand Y
A. A. Constraint Equations
Cases of Brand X require 7.5 units of nutrients and brand Y requires 7.5 units of nutrients.
So
Total nutrients to be used = 7.5X + 7.5Y
Units of N used ≤ 56.25
7.5X + 7.5Y ≤ 30 (First Equation)
Similarly
Cases of Brand X requires 6 units of flavor and brand Y requires 12 units of Flavor
Units of F used = 6X + 12Y
Units of F used ≤ 72
6X + 12Y ≤ 72 (Second equation)
Cases of Brand X requires 15 units of C and brand Y requires 6 units of Color
Units of C used = 15X + 6Y
Units of C used 90
6X + 15Y ≤ 90 (Third Equation)
Also Max 40X + 30Y
X, Y≥ 0
1. 1. For the nutrient:
7.5X + 7.5Y ≤ 56.25

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The maximum constraint: 7.5X + 7.5Y = 56.25
The minimum constraint: 7.5X + 7.5Y< 56.25
For the flavor:
When 12X + 6Y≤72,
The maximum constraint: 12X + 6Y = 72
The minimum constraint: 12X + 6Y < 72
For the Color
When 6X + 15Y ≤ 90
The a maximum constraint: 6X + 15Y = 90
The a minimum constraint: 6X + 15Y < 90
A. B. At the dotted line:
When X = 0, Y = 8 and when Y = 0, X = 6
Equation for profit line is:
6X + 8Y ≤ 48
When X = 3, Y = 4, the point (4,3) is a point on the profit line.
Total contribution to profit for Brand X per crate = $ 40 & brand Y = $30.
Total contribution to profit = No. of brand X crates sold ($40) + No. of brand Y
crates sold ($30).
Total contribution to profit = 40(3) + 30(4)
= $ 240
A. C. Optimal profit:

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