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?

---

Definitions:

Louis XIV

Known as the "Sun King," he was King of France from 1643 to 1715 and is noted for his centralized administration and lavish court at Versailles.

Personal Power

The ability of an individual to influence others and control their own life, often deriving from personal traits, skills, or positions of informal authority rather than formal hierarchical structures.

Grand Strategy

A comprehensive, overarching plan or policy designed to achieve major or overall objectives, particularly in politics or business.

Louis XIV

King of France from 1643 to 1715, known as the Sun King, he ruled for the longest time in European history and significantly influenced the course of French absolutism.