A Grain Store Has Six Types of Grain,each Varying in Cost,quality,and

question 75

Essay

A grain store has six types of grain,each varying in cost,quality,and nutritional content.Periodically,excess inventory of these grains are consolidated into two local products,Feed-M-All and Supreme-Feed.Feed-M-All sells for $6.50 for a 10-pound bag while Supreme-Feed sells for $8.50 for a 10-pound bag.These feeds are advertised as having the following nutritional content:
$\begin{array}{lcrc}\text { Grain } & \text { Minimum Protein } & \text { Minimum Fat } & \text { Maximum Carbohydrates } \\\hline \text { Feed-M-All } & 16 \% & 18 \% & 10 \% \\\text { Supreme-Feed } & 18 \% & 18 \% & 9 \%\end{array}$

The component grains have the following content characteristics:
$$\begin{array} { c c c c c c c } \text { Gran } & \text { Cost/10 lbs } & \text { Quality } & \text { Pratein } & \text { Fat } & \text { Carbohydrates } & \text { Paunds Avail. } \\\hline \text { A } & \$ 4.75 & 4 & 15 \% & 10 \% & 10 \% & 90 \\\mathrm {~B} & \$ 4.00 & 2 & 20 \% & 20 \% & 8 \% & 120 \\\mathrm { C } & \$ 3.75 & 1 & 10 \% & 25 \% & 5 \% & 150 \\\mathrm { D } & \$ 4.25 & 3 & 15 \% & 20 \% & 10 \% & 125 \\\mathrm { E } & \$ 4.50 & 3 & 20 \% & 20 \% & 10 \% & 85 \\\mathrm {~F} & \$ 5.00 & 4 & 25 \% & 15 \% & 12 \% & 165\end{array}$$
Targets for Feed-M-All are a cost of $ 4.35 per 10-pound bag,a quality rating of 2.25,along with the minimum percentages of protein and fat,and the maximum percentage of carbohydrates.Similar targets are set for Supreme- Feed with cost set at $ 4.60 and quality at 2.45.There must be at least a 70%-30% mix among these two local feeds.
Formulate an LP model for this product mix problem.

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Definitions:

Canadian Labor Relations

The system of laws, practices, and institutions that govern the relationships between employers, employees, and unions in Canada.

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The interactions and legal frameworks governing the relationships between workers, unions, and employers within the United States.

France's Labor Movement

The collective organization of workers in France aimed at advocating for workers' rights and improvements in labor standards.

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