A Company Has the Following Inputs and Cost Structure They Must Also Use the Following Minimum Quantities

question 12

Essay

A company has the following inputs and cost structure.
$$\begin{array} { l l l l } \text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\\text { Ingredient A } & 3 & 2 & 4 \\\text { Ingredient B } & 2 & 3 & 1 \\\text { Ingredient C } & 1 & 0 & 2 \\\text { Ingredient D } & 6 & 8 & 4 \\\text { Cost per unit } & 0.00125 & 0.0025 & 0.015625\end{array}$$ They must also use the following minimum quantities.
A 120, B 80, C 40, D 240
The is also a maximum of Z of 80 units.
a) Calculate how many of each product (X, Y, Z) should be produced.
b) How much is the minimized total cost?

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Definitions:

Heat

A form of energy that is transferred between systems or objects with different temperatures, flowing from the hotter system to the cooler one.

Organic Matrix

The non-mineral component of bones and teeth, comprising collagens and other organics, which gives them flexibility and tensile strength.

Acid

A substance that releases hydrogen ions (H+) in solution, characterized by a sour taste, ability to turn blue litmus paper red, and ability to react with bases to form salt and water.

Unravels Proteins

A process by which proteins are broken down into their constituent amino acids or peptides, typically through the action of enzymes or chemicals.