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Section 9.3
1) It is estimated that the weekly output of a certain plant is given by the function
units, where x is the number of skilled workers
Qxy
x
y xy x
y
(,)
=+
+
−
−
1200
500
23
2
and y the number of unskilled workers employed at the plant.
a) Find
∂
∂
Q
x
b) Find
∂
∂
Q
y
c) Find and interpret
∂
∂
Q
x
(,
)
100 50
d) When there are 30 skilled workers and 60 unskilled workers employed at the plant, how
rapidly is weekly output increasing with respect to the number of skilled workers.
2) Referring to the beef consumption example of section 9.1, when the household income is
$20,000 and the price of beef is $4.50, how rapidly is beef consumption changing with respect to
household income?
3) Referring to the function
from example 1, find
x
y
+
−
−
2
the second partial derivatives
.
Q xyQ xyQ xya
n
dQ xy
xx
xy
yx
yy
,
,
,
Section 10.2
1) Evaluate the determinant of each matrix:
a)
b)
31
0
21
61
10
−
2) The annual cost for labor and specialized robotics equipment for an automobile manufacturer,
in millions of dollars, is given by
, where x is
Cxy
x
x
y
y
x
y
.
=++
−−+
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 Fall '08
 Royer
 Calculus

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