An on-demand printing company has monthly overhead costs of $1200 in rent, $420 in electricity. $100 for phone service, and $200 for advertising and marketing. The priming cost is $40 per thousand Pages for paper and ink. a. Write a cost function to represent the cost C x for printing x thousand Pages for a given month. b. Write a function representing the average cost C ¯ x for printing x thousand Pages for a given month. c. Evaluate C ¯ 20 , C ¯ 50 , C ¯ 100 , and C ¯ 200 . d. Interpret the meaning of C ¯ 200 . e. For a given month, if the printing company could print an unlimited number of Pages, what value would the average cost per thousand Pages approach? What does this mean in the context of the problem?
An on-demand printing company has monthly overhead costs of $1200 in rent, $420 in electricity. $100 for phone service, and $200 for advertising and marketing. The priming cost is $40 per thousand Pages for paper and ink. a. Write a cost function to represent the cost C x for printing x thousand Pages for a given month. b. Write a function representing the average cost C ¯ x for printing x thousand Pages for a given month. c. Evaluate C ¯ 20 , C ¯ 50 , C ¯ 100 , and C ¯ 200 . d. Interpret the meaning of C ¯ 200 . e. For a given month, if the printing company could print an unlimited number of Pages, what value would the average cost per thousand Pages approach? What does this mean in the context of the problem?
An on-demand printing company has monthly overhead costs of
$1200
in rent,
$420
in electricity.
$100
for phone service, and
$200
for advertising and marketing. The priming cost is
$40
per thousand Pages for paper and ink.
a. Write a cost function to represent the cost
C
x
for printing x thousand Pages for a given month.
b. Write a function representing the average cost
C
¯
x
for printing x thousand Pages for a given month.
c. Evaluate
C
¯
20
,
C
¯
50
,
C
¯
100
,
and
C
¯
200
.
d. Interpret the meaning of
C
¯
200
.
e. For a given month, if the printing company could print an unlimited number of Pages, what value would the average cost per thousand Pages approach? What does this mean in the context of the problem?
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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