FinFone Paper Mill Is a Small-Scale Paper-Making Company Which Produces

question 43

Essay

FinFone Paper Mill is a small-scale paper-making company which produces four different types of paper. Each type of paper must go through processing on four different machines. The manufacturing time (in minutes) per unit of paper produced is listed in the following table. Time required (in minutes)
Paper Type
$\begin{array}{ccccc}\text { Machine Type } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline 1 & 2.4 & 1.2 & 2.7 & 3.2 \\2 & 2.1 & 2.4 & 3.2 & 3.3 \\3 & 1.6 & 0.9 & 2.6 & 5.1 \\4 & 2.5 & 2.5 & 3.2 & 6.5\end{array}$ ​
The maximum time allotted for each machine is 30 hours per week and at least 100 units of each type of paper should be made during the week.
Profit per unit is: $$\begin{array} { l c c c c } \text { Paper Type } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline \text { Profit } ( \$ ) & 0.25 & 0.32 & 0.44 & 0.5\end{array}$$ ​
Develop and solve an all-integer model that will determine, using the available machine time, the number of units of each paper type to be produced in order to meet the weekly demand and to maximize the profit.

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Definitions:

Henri Fayol

A French industrialist and management theorist renowned for developing a general theory of business administration.

Scalar Chain

A hierarchy of authority in an organization where every employee has a clear superior and subordinate, forming a direct vertical line of authority.

Unity of Command

A principle stating that each employee should receive orders from only one superior to avoid confusion and conflict.

Bureaucratic Organization

A form of organization characterized by a hierarchical structure, formal rules and policies, and an emphasis on administrative tasks and procedural correctness.