From past experience, a publisher knows that a particular type of book will sell 14,000 copies at a price of $20 each. Market research further indicates that for every one-dollar increase in price, sales will fall by 400 copies. The publisher asks for your advice in deciding the suggested retail price of the next book published.1
- Press the Y= key and enter the function into Y1= as (14000-400x)(20+x). Your screen should look like this:
- Press the WINDOW key and enter the values below. This will ensure a freindly window for this graph.
- Now press GRAPH to see the graph.
In the graphic shown here, the x-axis represents the number of
increases and the y-axis represents the total revenue from sales.
- Now press the TRACE key. The display will change so that the function, the value of x (number of increases) and y (revenue) are shown.
To stop the animation (for Netscape 2.0 and
above), click the stop button in the browser menu bar or tap
the Esc-key on the keyboard.
Notice that the revenue (Y) increases from $280,000 to $302,400 at seven increases and also at eight increases. After eight increases, the revenue begins to decrease.
Further analysis of this situation may be accomplished by a symbolic analysis, or by a numerical analysis.
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Problems of this type may be found in Mathematical Analysis, 3rd. Ed. By Arya and Lardner, published by Prentice Hall, 1989, page 93. |
