A cleaning company charges $ 100 for each office it cleans. The fixed monthly cost of $ 480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $ 52 per office and includes labor, gasoline, and cleaning supplies. (See Example 9) a. Write a linear cost function representing the cost C x in $ to the company to clean x offices per month. b. Write a linear revenue function representing the revenue R x in $ for cleaning x offices per month. c. Determine the number of offices to be cleaned per month for the company to break even. d. If 28 offices are cleaned, will the company make money or lose money?
A cleaning company charges $ 100 for each office it cleans. The fixed monthly cost of $ 480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $ 52 per office and includes labor, gasoline, and cleaning supplies. (See Example 9) a. Write a linear cost function representing the cost C x in $ to the company to clean x offices per month. b. Write a linear revenue function representing the revenue R x in $ for cleaning x offices per month. c. Determine the number of offices to be cleaned per month for the company to break even. d. If 28 offices are cleaned, will the company make money or lose money?
A cleaning company charges
$
100
for each office it cleans. The fixed monthly cost of
$
480
for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is
$
52
per office and includes labor, gasoline, and cleaning supplies. (See Example 9)
a. Write a linear cost function representing the cost
C
x
in $
to the company to clean
x
offices per month.
b. Write a linear revenue function representing the revenue
R
x
in $
for cleaning
x
offices per month.
c. Determine the number of offices to be cleaned per month for the company to break even.
d. If 28 offices are cleaned, will the company make money or lose money?
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
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