Math 1P97. Assignment 3 (4%).
Due date: Monday, June 6, 6:45pm
Student’s name:
Total mark:
NOTE:
Students are expected to complete ALL questions on the assignment. However, only a subset
of questions will be considered for marking. Marks will be deducted for incomplete assignments.
Show all
your work.
1. (Marginal cost, revenue, and proﬁt) Pulsar manufactures a series of 20inch ﬂattube digital televi
sions. The quantity
x
of these sets demanded each week is related to the wholesale unit price
p
by
the equation
p
=

0
.
003
x
+ 150. The weekly total cost incurred by Pulsar for producing
x
sets is
C
(
x
) = 0
.
000004
x
3

0
.
006
x
2
+ 150
x
+ 60
,
000 dollars.
a) Find the revenue function
R
=
R
(
x
) and the proﬁt function
P
=
P
(
x
).
b) Find the marginal cost function, the marginal revenue function, and the marginal proﬁt function.
c) How many TVs should be produced to maximize the proﬁt?
2. Refer to the following graph of a function
y
=
f
(
x
):
a) ﬁnd the points where
f
(
x
) = 0
b) ﬁnd the intervals where
f
0
(
x
)
>
0
c) ﬁnd the intervals where
f
0
(
x
)
<
0
d) ﬁnd the points/intervals where
f
0
(
x
) = 0
e) ﬁnd the points where
f
0
(
x
) doesn’t exist.
f) ﬁnd the points/intervals where
f
00
(
x
) = 0.
j) ﬁnd the intervals where
f
00
(
x
)
>
0.
h) ﬁnd the intervals where
f
00
(
x
)
<
0.