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

question 85

Essay

A company has the following inputs and cost structure.
$$\begin{array} { l l l l } \text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\\text { Ingredient A } & 4 & 2 & 4 \\\text { Ingredient B } & 2 & 2 & 1 \\\text { Ingredient C } & 1 & 5 & 3 \\\text { Ingredient D } & 6 & 8 & 7 \\\text { Cost per unit } & 0.05 & 0.017 & 0.045\end{array}$$ They must also use the following minimum quantities.
A 80, B 64, C 90, D 120
The is also a maximum of Z of 100 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:

Recall

The ability to retrieve and reproduce information or experiences from one's memory.

Laissez-Faire

An economic theory advocating minimal government intervention in the affairs of private businesses and individuals.

Moralizing

The act of expressing or teaching moral values, often involving making judgments about what is right or wrong behavior and imposing these standards on others.

Punishment

A consequence applied with the intention of reducing or eliminating an unwanted behavior, often employed in legal and educational contexts.