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

question 62

Essay

A company has the following inputs and cost structure.
$$\begin{array} { l l l l } \text { Product } & \mathrm { X } & \mathrm { Y } & \mathrm { Z } \\\text { Ingredient A } & 4 & 2 & 8 \\\text { Ingredient B } & 2 & 3 & 3 \\\text { Ingredient C } & 4 & 5 & 3 \\\text { Ingredient D } & 7 & 5 & 7 \\\text { Cost per unit } & 0.25 & 0.21 & 0.69\end{array}$$ They must also use the following minimum quantities.
A 100, B 120, C 140, D 160
The is also a maximum of Z of 200 units.
c) Calculate how many of each product (X, Y, Z) should be produced.
d) How much is the minimized total cost?

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Definitions:

Utility

A measure of satisfaction or pleasure that a consumer obtains from consuming goods and services.

Coffee

A brewed drink prepared from roasted coffee beans, the seeds of berries from certain Coffea species, consumed worldwide for its stimulating effects.

Donuts

A sweet, fried or baked pastry often shaped in rings or filled with various sweet fillings.

Price Ratio

Price Ratio is a comparative metric that divides the price of one good, asset, or commodity by another, often used to assess relative value or performance.