A Small Foundry Has Received an Order for an Iron

question 10

Essay

A small foundry has received an order for an iron alloy called Falloy which has the following specifications:
$\begin{array} { l l } \text { Content } &{ \text { Specification } } \\\hline\text { Nickel } & 5 \% \\\text { Manganese } & 4 \% \\\text { Copper } & 1 - 2 \% \\\text { Impurities } & { \text { no more than 3\% } } \\\text { Iron } & { \text { the balance } }\end{array}$
Falloy can be produced from the following inputs (balance to 100% consisting of iron).
$\begin{array} { l l } \text { Content } &{ \text { Specification } } \\\hline\text { Nickel } & 5 \% \\\text { Manganese } & 4 \% \\\text { Copper } & 1 - 2 \% \\\text { Impurities } & { \text { no more than 3\% } } \\\text { Iron } & { \text { the balance } }\end{array}$

Formulate the linear programming problem that will indicate the blending "recipe" that will minimize the cost of this alloy.

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Definitions:

Trade-in Allowance

The discounted price offered when a customer gives a used item as part of the payment for a new item, reducing the cash cost of the new purchase.

Book Value

The net value of a company's assets minus its liabilities, often used to assess the company's worth.

Gain

A financial increase or profit, particularly from the sale of investments or assets, not typically related to the entity’s primary operations.

Extraordinary Repair

A significant restoration or overhaul that extends an asset's useful life beyond its original forecast.