M119 Chapter 1 Review
1. At a certain factory, the total cost of
manufacturing q units during the
daily production
run is
dollars. On a typical workday, 
units are
manufactured during the first t hours of a production run.
a)
Find the cost as a function of time.
b)
How much is spent during the first 3 hours of production.
2. Suppose the total cost (in dollars) of
manufacturing q units of a certain
commodity is
given by the function 
. What is the cost of
producing the
10th unit of the commodity?
3. What is the domain of the function 
?
4. Find the domain of the function 
.
5. Since the beginning of the year, the price of
a carton of eggs has been rising at a
constant rate of 1.5 cents per month. By May 1, the price had reached 90 cents per
carton.
Express the price of eggs as a function of time in months and determine
the
price at the beginning of the year. [month 1]
6. An appliance manufacturer can sell
refrigerators for $600 each. The
manufacturer’s
total cost consists of a fixed overhead of
$12,000 plus production costs of $400 per
refrigerator. How many refrigerators must be sold for the
manufacturer to break even?
7. A cylindrical can is to have volume of 
cubic inches. The cost of the material used
for the top and bottom of the can is 4
cents per square inch, and the cost of the
material used for the curved side is 3
cents per square inch. Express the cost
of
constructing the can as a function of its
radius.
8. A closed cylindrical can has a surface area
of 
square inches. Express the
volume of the can as a function of its
radius.
9. A farmer is planning to plant a rectangular
garden with an area of 4,000 square yards.
The garden is to be fenced on all four
sides. Express the number of yards of
fencing
required as a function of the length.
10. For the function 
, find f(0),
f(1), and f(3) and graph the
function.
11. A ball is thrown directly upward from the
edge of a cliff in such a way that t
seconds
later, it is 
feet above the
ground. Sketch the graph of s(t) and
determine the maximum height attained by
the ball.
12. An efficiency study of the morning shift at a
certain factory indicates that an average
worker who arrives on the job at 8:00
a.m. will have assembled
transistor radios x hours later. How many radios will such a
worker assemble between 10:00 and 11:00
a.m.?
13. A manufacturer can produce cassette tape
recorders at a cost of $20 apiece. It is
estimated that if the tape recorders are
sold for x dollars apiece, consumers
will buy
276
– x of them a month. Express the
manufacturer’s monthly profit as a function of
price, graph this function, and use the
graph to estimate the optimal selling price.
What is the maximum profit?
14. A closed box with a square base is to have a
volume of 110 cubic meters. The
material for the top and bottom of the
box costs $20 per square meter, and the
material for sides cost $15 per square
meter. Express the construction cost of
the
box as a function of the length of its
base.
15. A manufacturer of self-baiting mousetraps is
currently selling 1,500 traps a month to
retailers at a price of $1 per
trap. She estimates that for each 1 cent
increase in
price, she will sell five fewer traps
per month. The traps cost 30 cents each
for labor
and materials. Find the profit P(x) as a function of the price increase x. Graph the
function to find the new selling price
where the maximum profit occurs.
Solutions:
1. a)
b) $3,000 2. $228
3. 
4. 
5. p(t)=1.5t + 82.5; $.84 6. 60 refrigerators
7. 
8. 
9. 
10. f(0)=
-1; f(1) = 1; f(3)
= 11 ![[image]](Chapter%201%20Review_files/image034.jpg)
11. 288 feet 12.
22 radios
13. 
; $148; $16,384
14. 
15. 
; n=115; price is $2.15