Functions and Models
 Function Evaluator and Grapher
 Excel Grapher (downloadable Excel workbook) For the Excel grapher to work, macros need to be enabled when you open the page.
Functions that we use to represent real life situations, like the function we used in the preceding tutorial to talk about Facebook membership, are mathematical models.
Cost, Revenue and Profit Models
Take a look at the third example above, where the total cost of purchasing a number of items (sodas) was expressed as a function of the number of items x. This function is an example of a cost function. The rest of this explanation will appear here only after you correctly entered the function in the third example above.
Cost Function
A cost function specifies the cost C as a function of the number of items x. Thus, C(x) is the cost of x items, and has the form


Example
The daily cost to your company to print x paperback scifi novels is Note that C is measured in dollars, and x is measured in books (paperback scifi novels, to be precise). The marginal cost is m = and the fixed cost is b = 

Revenue Function The revenue resulting from one or more business transactions is the total payment received, sometimes called the gross proceeds. If R(x) is the revenue from selling x items at a price of m each, then R is the linear function R(x) = mx and the selling price m can also be called the marginal revenue. 

Example
Suppose that your publishing company sells scifi paperbacks to a large retailer for per book. Then


Profit Function
The profit is the net proceeds, or what remains of the revenue when costs are subtracted. If the profit depends linearly on the number of items, the slope m is called the marginal profit. Profit, revenue, and cost are related by the following formula.


Example
Going back to the scifi novels, we already have the cost and revenue functions:

Sometimes if it more convenient to express models in equation form:
Function and Equation Form of Mathematical Models
As an example, take a look at the above cost and revenue functions again:
Here, the independent variable is x, and the dependent variables are C and R. Function notation and equation form, using the same letter for the function name and the dependent variable, are often used interchangeably, so we can say, for example, that the cost equation above specifies C as a function of x. 
The next quiz example is similar to Example 2 in Section 1.2 of :
You are the manager of Sassy Surf Creations, a new trendsetting clothing manufacturer. The cost function for your very exclusive Tai Kwon Do Dragon T shirts is dollars, and you sell the shirts for each. Take a look at the graphs of cost and revenue below the questions to assist you in answering them, but you need to use the formulas to give the exact answers.
Revenue and Cost Functions

Copyright © 2009 Stefan Waner