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:

Cost Savings

The reduction in expenses achieved through efficiency improvements, negotiation, or eliminating wasteful practices.

Productivity Measurement

The process of determining the efficiency of production of goods or services, typically by comparing input resources to output.

Evaluation System

A structured approach to assess the performance and effectiveness of employees, projects, or processes.

Goal Setting

The process of identifying specific, measurable, achievable, relevant, and time-bound objectives to be accomplished.