1
Math 11
Scimmage Test 1
1.)
The variable cost to manufacture an item is
$10
, and it costs
$2, 500
to produce
100
items.
Write the cost function, then use it to estimate the cost of manufacturing
300
items.
2.)
A firm producing video tapes has fixed costs of
$6, 800
, and a variable cost of
30
cents
per
tape. If the video tapes sell for
$2
each, find the number of tapes that must be produced to
break-even.
3.) A person takes three daily vitamin supplements, B, C, and E, via three types of pills,
regular, extra strength, and fortified. Each regular pill contains
10
units of B,
20
units of C
,
and
20
units of E. Each extra strength pill contains
20
units of B,
60
units of C
,
and
10
units of E. Each fortified pill contains
10
units of B,
20
units of C
,
and
40
units of E. How
many pills of each type should be taken in order to achieve
50
units of B,
120
units of C
,
and
90
units of E?
Set up the sytem of equations, and write the augmented matrix for the system.
4.)
Let
A
(0,2) and
B
(3,0). Find the equation of the line through
A
perpendicular to the line
containing
A
and
B
.
5.)
A firm produces a machine for $50,000 and the machine has a useful life (determine by tax
laws) of ten years. If the machine depreciates $4,000 per year, find:
a.)
The value of the machine,
V
, after
t
years.
b.)
Find
V
(10), the salvage value of the machine.
6.) A travel Agency is planning charter flights to Hawaii for exactly 1400 passengers aboard two
types of jets. Each 747 jet holds 400 passages
and each 707 holds 150 passengers. The rental
fee is $15,000 for each 747 and $9,000 for each 707. If exactly $66,000 must be used for renting
the jets, how many of each type should be ordered?
7.) A woman wants to use milk and orange juice to increase the amount of calcium and
vitamin A in her daily diet. An ounce of milk contains
37
milligrams mg
( )
of calcium and
57
micrograms
μ
g
( )
of vitamin A. An ounce of orange juice contains
5
mg
of calcium and
65
μ
g
of vitamin A. How many ounces of milk and orange juice should the woman drink
each day to provide exactly
500
mg
of calcium and
1, 200
μ
g
of vitamin A?
Set up the sytem of equations, and write the augmented matrix for the system.
8.) A shoe company makes special shoes for runners, hikers, and bikers on three different
machines. Each running shoe requires 1 hour on each machine; each hiking shoe requires 2
hours on machine A, 1 hour on machine B, and 2 hours on machine C; each biking shoe
requires 2 hours on machine A, 1 hour on machine B, and 1 hour on machine C. Machine A is
available exactly 26 hours a week, machine B 21 hours a week, and machine C 23 hours a
week. How many shoes of each type can be made each week?
9.)
The sum of the digits of a two-digit number is 14. If the digits are reversed, the value of the
number is decreased by 18. Find the number. (
Use system of equations
)
[
Hint: if xy is two-digit number, then the value of xy is 10x + y
]