The Alpha Beta Corporation Makes Laser and Inkjet Printers for Personal

question 13

Essay

The Alpha Beta Corporation makes laser and inkjet printers for personal computers. Each laser printer yields $40.00 in profits and each ink jet printer provides $20.00. Each of the printers goes through two assembly areas. The following table provides processing times per unit (in minutes) as well as total available processing times per department:
$\begin{array}{lcc}\text { Printer }&\text { Dept. A }&\text { Dept. B }\\\text { Laser } & 9 & 12 \\\text { Inkjet } & 6 & 8 \\\text { Total time per day } & 216 & 384\end{array}$
Sales commitments require at least 5 laser printers and 10 inkjet printers to be made per day. The company is interested in determining how many of each printer to produce so as to maximize its profit.
a. What is the objective function for this LP problem?
b. What are the constraints corresponding to Dept. A if x₁ corresponds to laser printers?
c. What are the optimal solution points for this problem?
d. What is the optimal value of the objective function?

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Definitions:

Natural Conditions

Environmental or ecological circumstances not influenced or modified by human activities, often serving as a baseline or control in scientific studies.

Objective Introspection

The process of examining one's own thoughts and feelings from an objective standpoint, as a means of understanding one's inner world.

Valid Experiment

An experiment that is methodologically sound, properly controlled, and capable of being replicated to test its results.

Gestalt Psychology

A psychological approach that emphasizes understanding the mind and behavior as a whole, rather than dissecting them into parts.