Marginal Cost and Time Rate of Change The cost of manufacturing x cases of cereal is C dollars, where C = 3 x + 4 x + 2 . Weekly production at t weeks from the present is estimated to be x = 6200 + 100 t cases. Find the marginal cost, d C d x . Find the time rate of change of cost, d C d t . How fast (with respect to time) are costs rising when t = 2 ?
Marginal Cost and Time Rate of Change The cost of manufacturing x cases of cereal is C dollars, where C = 3 x + 4 x + 2 . Weekly production at t weeks from the present is estimated to be x = 6200 + 100 t cases. Find the marginal cost, d C d x . Find the time rate of change of cost, d C d t . How fast (with respect to time) are costs rising when t = 2 ?
Solution Summary: The author explains how to determine the cost of manufacturing x cases of cereal and the weekly production at t weeks from the present.
Marginal Cost and Time Rate of Change The cost of manufacturing
x
cases of cereal is
C
dollars, where
C
=
3
x
+
4
x
+
2
. Weekly production at
t
weeks from the present is estimated to be
x
=
6200
+
100
t
cases.
Find the marginal cost,
d
C
d
x
.
Find the time rate of change of cost,
d
C
d
t
.
How fast (with respect to time) are costs rising when
t
=
2
?
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
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