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:

Exercising The Option

The act of buying or selling the underlying asset via the option contract.

Employee Stock Option (ESO)

An option granted to an employee by a company giving the employee the right to buy shares of stock in the company at a fixed price for a fixed time.

European Options

Financial derivatives that give the holder the right, but not the obligation, to buy or sell an underlying asset at a specified price on the expiration date, unlike American options which can be exercised at any time before expiry.

European Options

Options that can only be exercised at the expiration date, not before.