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Calculus 1
3.10 Business and Economics Applications
Name: _______________________
Date: _________________
Period: ____________
Objective: At the end of this lesson, you should be able to: Apply calculus concepts to solve
business applications.
Basic Business Terms and Formulas
x
p
R
C
C
P
Break Even Point dR dC dP
,
,

dx dx dx
Example 1: A manufacturer determines that the profit derived from selling x units of a certain
item is given by P  0.0002 x 3  10 x. Find the marginal profit for a production level of 50 units,
and compare this with the actual gain in profit obtained by increasing the production from 50 to
51 units.
(over)
Finding the Marginal Revenue
Example 2: A fast-food restaurant has determined that the monthly demand for its hamburgers is
60000  x
p
. Find the increase in revenue per hamburger (marginal revenue) for monthly
20000
sales of 20000 hamburgers.
Finding Marginal Profit
Example 3: Suppose the cost of producing x hamburgers from example 2 is C  5000  0.56x.
Find the total profit and the marginal profit for 20000, for 24400, and for 30000 hamburgers.
Hamburgers
Profit
Marginal Profit
20000
24400
30000
Calculus 1
3.10 Business and Economics Applications
(continued)
Name: _______________________
Date: _________________
Period: ____________
Finding the Maximum Profit
Example 4: In marketing a certain item, a business has discovered that the demand for the item
50
is represented by p 
. The cost of producing x items is given by C  0.5x  500. Find the
x
price per unit that yields a maximum profit.
Minimizing the Average Cost
Example 5: A company estimates that the cost (in dollars) of producing x units of a certain
product is given by C  800  0.04 x  0.0002 x 2 . Find the production level that minimizes the
average cost per unit.
HW: 3-28