University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA33
Assignment 7
Winter 2008
Quiz 7 is based on this assignment and the relevant text readings and lecture notes.
Quiz 7 will
be written in the 8th tutorial, which takes place during the week of March 10  14.
Study:
Sections 17.3 and 17.4 for this assignment (reviewing sections 17.1 and 17.2 would be useful
too). Read ahead in Sections 17.5 and 17.6.
Problems:
1. Section 17.3, Pages 759  761 # 1,
2,
4  10,
14,
18  20.
2. Section 17.4, Page 763 # 1,
2,
5,
6,
10,
11,
13,
14,
16,
19.
3. Find the equation of the horizontal plane that is tangent to the graph of the function
z
=
G
(
x, y
) =
x
2

4
xy

2
y
2
+ 12
x

12
y

1 . (Hint: review the general form of a plane in
3dimensional space as stated at the bottom of page 748).
4. Let
P
(
x, y
) =
xy
ax
+
by
where
P
represents profit;
x, y >
0 represent sales of products
X
and
Y
(respectively); and
a, b >
0 are constants. Show that the sum of the marginal profits when
x
=
y
is equal to
1
a
+
b
5. Throughout this problem use the function in #24 on page 796
(a) Do problem # 24 on page 796
(b) Verify the concept of marginal as outlined at the top of page 756. That is, verify that
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 G
 Math, Derivative, Binary relation, Computer & Mathematical Sciences, relevant text readings

Click to edit the document details