1. 2-8 MATHEMATICALLY MODELING A BUSINESS
Banking
11/19/2018
2-8 MATHEMATICALLY MODELING A BUSINESS
OBJECTIVES
Recognize the transitive property of dependence as it is used in a business model.
Use multiple pieces of information, equations, and methodologies to model a new business.
Chapter 1

2. Key Terms
dependence
transitive property of dependence

3. How can you mathematically model a start-up business?
Name other situations that illustrate dependence.
Using the situations identified in previous discussions, illustrate how they might be examples of the transitive property of dependence.

4. Example 1
Determine the expense, E, for production of an item when the price, p, is $60 given E = 50q + 80,000 and q = 80p + 100,000.

5. CHECK YOUR UNDERSTANDING
Determine the expense, E, for production of an item when the price, p, is $42 given E= 50q + 80,000 and q = 80p + 100,000.

6. EXTEND YOUR UNDERSTANDING
Suppose A = 20x + 30, x = 30y + 40, and y = 40z Describe how the value of A depends on the value of z.

7. Example 2
A business model uses a summary analysis of the situation in terms of dependent variables. Examine the three graphs of a business situation for the production of widgets. The graphs depict numerical information that is needed to complete the summary analysis.
Write the summary analysis in terms of the data presented in the graphs. The summary analysis should have the following format.
In summary, to start this business, __?__ widgets should be manufactured. Each should be sold for $__?__.
The breakeven point is reached at a price of $__?__ or $__?__, but a profit is made at any price between those prices.
At the selling price, there is revenue of $__?__ and expenses of $__?__, resulting in a profit of $__?__.

9. CHECK YOUR UNDERSTANDING
Use the points labeled on the graphs to show that the maximum profit at the selling price is the difference between the revenue and expense values at that price.