1. 3.10 Business and Economic Applications

2. Basic Terms:
x: # units produced (or sold)
p: price per unit
R: total revenue from selling x units (R=xp)
C: total cost of producing x units
C: average cost per unit
P: total profit from selling x units (P = R – C)
Break even points: # units for which R = C

3. Marginals:

4. A manufacturer determines that the profit derived from selling x units of a certain item is given by P=0.0002x3 + 10x.
a.) Find the marginal profit for a production level of 50 units.
b.) Compare this with the actual gain in profit obtained by increasing the production from 50 to 51 units.

5. A fast-food restaurant has determined that the monthly demand for its hamburgers is
Find the increase in revenue per hamburger (marginal revenue) for monthly sales of 20,000 hamburgers.

6. Suppose the cost for producing x hamburgers is
Find the total profit and marginal profit for
20,000, 24,400, and 30,000 units.

7. Marginal Profit (dP/dx) $0.44 -$0.56
Suppose the cost for producing x hamburgers is
Find the total profit and marginal profit for
20,000, 24,400, and 30,000 units.
Demand(x)
20,000
24,400
30,000
Profit (P)
$23,800
$24,768
$23,200
Marginal Profit (dP/dx)
$0.44
-$0.56

8. In marketing a certain item, a business has discovered that the demand for the item is represented by
The cost of producing x items is given by C=0.5x Find the price per unit that yields a maximum profit.

9. In marketing a certain item, a business has discovered that the demand for the item is represented by
The cost of producing x items is given by C=0.5x Find the price per unit that yields a maximum profit.

10. Homework
Handout (3.10)
#3, 5, 7, 11, 20, 21