A Grain Store Has Six Types of Grain, Each Varying

question 82

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:
$\begin{array}{lccc}\text { Grain } & \text { Minimum Proten } &\text { Minimum Fat }&\text { Maximum Carbohydrates }\\\hline\text { Feed-M-All } & 16 \% & 18 \% & 10 \%\\ \text {Supreme-Feed} &18 \%&18 \% &9 \% \\\end{array}$
The component grains have the following content characteristics:
$$\begin{array} { c c c c c c c } \text { Grain } &\text { Cost/10lbs }& \text { Quality } & \text { Praten } & \text { Fat } & \text { Carbohydrates } & \text { Paunds Ayail. } \\\hline \mathrm { A } & \$ 4.75 & 4 & 15 \% & 10 \% & 10 \% & 90 \\\mathrm {~B} & \$ 4.00 & 2 & 20 \% & 20 \% & 8 \% & 120 \\\mathrm { C } & \$ 3.75 & 1 & 10 \% & 25 \% & 5 \% & 150 \\\mathrm { D } & \$ 4.25 & 3 & 15 \% & 20 \% & 10 \% & 125 \\\mathrm { E } & \$ 4.50 & 3 & 20 \% & 20 \% & 10 \% & 85 \\\mathrm {~F} & \$ 5.00 & 4 & 25 \% & 15 \% & 12 \% & 165\end{array}$$ 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:

Mere Exposure Effect

A mental effect where individuals grow fond of something simply due to their familiarity with it.

Social Traps

Situations where a group or individual acts in a way that seems beneficial in the short term but leads to negative outcomes in the long term for everyone involved.

Just-world Phenomenon

The cognitive bias that a person's actions are inherently inclined to bring morally fair and fitting consequences to that person, to the end of all noble actions being rewarded and all evil actions punished.

Altruism

The selfless concern for the well-being of others, often leading to actions for their benefit without personal gain.