Demand
- Numerical Analysis -
- TI-83 Procedure -

Situation:

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

Calculator Procedure:

1. Press the Y= key and enter the function into Y1= as (14000-400x)(20+x). Your screen should look like this:
   
   
   
   
2. Press the 2nd TblSet keys and enter 0 for TblStart and 1 for deltaTbl.
   
   
   
   
3. Now press 2nd TABLE to see the table.
   
   
   

In the graphic shown here, X represents the number of $1 increases in the price of the book. Y₁ represents the total revenue from book sales.

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 (Y1) 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 graphing the function listed above, or by a symbolic analysis. The numerical analysis may be modeled without the calculator.

1	Problems of this type may be found in Mathematical Analysis, 3rd. Ed. By Arya and Lardner, published by Prentice Hall, 1989, page 93.