1
MATH 119
Chapter 4: Derivative Applications
Class Note
Ex 1:
Read example 3 and 4 on page 191.
Ex 2:
An appliance firm determines to sell
q
radios, the price per radio is given by
p
= 300 
q
it also
determines that the total cost of producing
q
radios is given by:
C(q)
= 1000 + 0.5
q
2
.
a) find the total revenue function
b) find the total profit function (
P
=
R

C
)
c) how many radios must be produced and sell to maximize the profit
d) what is the maximum profit? (When
P
' = 0 or when
R
' =
C
' as in section 2.6)
e) what is the price per radio must be charged to maximize the profit?
Ans: a) R = 300q  q
2
.
b) P = 1.5q
2
+ 300q 1000.
c) 100.
d) 14000
e) 200.
Ex 3:
A theater determine that if the admission price
is $ 10, it averages 100 people in attendance. But for every
increase of $ 2, it loses 5 customers from the average number. Every customers spends an average of $ 2 on
concessions. What admission price should the theater charge in order to maximize the revenue?
Solution:
•
Revenue from tickets
=
(New Price) (New # of tickets)
=
(10 + 2
x
) (100  5
x
)
•
Revenue from concessions
=
$ 2 (New # of customers)
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 Fall '09
 MaanOmran
 Derivative, Revenue

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