Project 21
Joey Koons Runs a Small Custom Computer Parts Company

question 19

Essay

Project 2.1
Joey Koons runs a small custom computer parts company. As a sideline he offers customized and pre-built computer system packages. In preparation for the upcoming school year, he has decided to offer two custom computer packages tailored for what he believes are current student needs. System A provides a strong computing capability at a reasonable cost while System B provides a much more powerful computing capability, but at a higher cost. Joey has a fairly robust parts inventory but is concerned about his stock of those components that are common to each proposed system. A portion of his inventory, the item cost, and inventory level is provided in the table below.
The requirements for each system are provided in the following table:
$$\begin{array} { l c c } & \text { System } \mathrm { A } & \text { System B } \\\hline \text { Processor } & 366 \mathrm { MHZ } & 700 \mathrm { MHZ } \\\text { Memory } & 64 \mathrm { MG } & 96 \mathrm { MG } \\\text { Hard Drive } & 6 \mathrm {~GB} & 20 \mathrm {~GB} \\\text { Monitor } & 15 \mathrm { " } & 15 \text { " } \\\text { Graphics Card } & \text { Stock } & \text { Stock } \\\text { CD-ROM } & 40 \mathrm { X } & 72 \mathrm { X } \\\text { Sound Card } & \text { Stock } & \text { Stock } \\\text { Speakers } & \text { Stock } & 60 W \\\text { Modem } & \text { Stock } & \text { Stock } \\\text { Mouse } & \text { Stock } & \text { Stock } \\\text { Keyboard } & \text { Stock } & \text { Stock }\end{array}$$ Each system requires assembly, testing and packaging. The requirements per system built and resources available are summarized in the table below.
$$\begin{array} { l c c c } & \text { System A } & \text { System B } & \text { Total Hours Available } \\\hline \text { Assembly (hours) } & 2.25 & 2.50 & 200 \\\text { Testing (hours) } & 1.25 & 2.00 & 150 \\\text { Packaging (hours) } & 0.50 & 0.50 & 75\end{array}$$ Joey is uncertain about product demand. In the past he has put together similar types of computer packages but his sales results vary. As a result is unwilling to commit all his in-house labor force to building the computer packages. He is confident he can sell all he can build and is not overly concerned with lost sales due to stock-outs. Based on his market survey, he has completed his advertising flyer and will offer System A for $ 1250 and will offer system B for $ 2325. Joey now needs to let his workers know how many of each system to build and he wants that mix to maximize his profits.
Formulate an LP for Dave's problem. Solve the model using the graphical method. What is Dave's preferred product mix? What profit does Dave expect to make from this product mix?

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Definitions:

Odds Ratio

A measure of association between an exposure and an outcome, indicating the odds of an outcome occurring with an exposure compared to without.

Myopia

A common eye condition characterized by difficulty seeing distant objects clearly, typically correctable with glasses or contact lenses.

Binomial Probability

The probability of achieving a specific number of successes in a fixed number of independent trials, each with two possible outcomes.

Observational Study

A study where the researcher observes and records behavior without manipulating variables or assigning interventions.