Math 1090.04 Exam 01
Spring 2013
Student ID Number:
Name
Instructions:
• Please remove headphones and hats during the exam
• Show all work, as partial credit will be given where appropriate. If no
work is shown, there may be no credit given.
• All final answers should be written in the space provided on the exam and
in simplified form. When needed give your answer as an exact amount,
, except for dollar amounts
2
i.e., a fraction or symbolic expression like e
which should be rounded to the nearest cent.
• CALCULATORS ARE NOT ALLOWED ON THIS EXAM
• This is a “closed notes/closed book” exam You are not allowed any
outside aids during this exam. If you have papers at your desk during
the exam you will be given a zero on the exam.
-
• If your phone is out during the exam it will be considered a
cheating offense put your phone away!
-
1. Given: f(x)
d
22 Febrilary 2013
Exam 01, Page 2 of 7
MathlO9O.004
=
j:
2x + 5 and g(x)
=
[pointsl
3x +4. Find f(g(3))
&((x a(x+4S
f(g(3))=
+ILjj
—
1.
fl12:
2(I34S
X
[points]
2. A manufacturer sells bracelets for $50 per bracelet. The fixed costs are $10,000 per
month and the variable costs are $30 per bracelet.
(a) Write the revenue equation described by this scenario
(a)60X
u.Loo
(b) Write the Cost equation described by this senario
(b)
c(x)
1 000
3bx-tiO
0
equation described by this scenario
(c) ‘Write the
P.()R (X) —CC,i)
PCx)
(c)
x— (Ox* jO0O0)
-
(d) How many bracelets must the manufacturer sell in order to break even?
k1YLA)
It
PLX)
‘---
P(i)= 2x_10b0OO
±
(d)
tO
Ot)
1
ZOx
O
60 O
(e) What will his revenue be wn he breaks even?
—
-
(e)
5OQ0
0
22 February 2013
Exam 01, Page 3 of 7
MathlO9O.004
3. Retailers will buy 5 jackets from a wholesaler if the price is $30 each, but only 2 jackets [ points]
if the price is $40 each. The wholesaler will supply 100 jackets at $60 each and 200
jackets at $110 each.
Write the SIui equation described above in slope-intercept form using the standard p
and q notation.
(O(O)
3.
-p --LO
0
(zp-)
‘1::
O-(OO
10
2cO_10O
9)
?
-
m
-
(p_
p
4. Find the market equilibrium for the demand and supply functions, where p is price and [ points]
q is quantity
Demand: p=—2q+ 220
Suppy:p=8q+10
0
p
4.
7
(o
l-1-e-rs
—z(I+o -4+O
lvi at hi 090.004
22 February 2013
Exam 01, Page 4 of 7
[pointsl
5. Following the steps below, find both the maximum aid minimum of the objective
function P(x, y) = x + y given these constraints:
y<—x+7
(1)
yx—2
(2)
x1
(3)
(a) Graph the feasible region using a test point on the graph provided.
SHOW YOUR WORK
Test Point Choice:
(a) (2:1)
Label Your Lines
iZIEiH
fLi
±Li
±±f.
I
..J..
LLLI
-±±ft
*±+*±±±--1-1+j±: iL2t[ H
•J-± i”t 1:i•
J_
L4
.
.
-
-
L
L
vA+i4‘
C,
.
\
E;It
IT
T-fftr
+I
-
i—r
T
1
.
!
—t
“ri
÷
E ±±1 1:’
4..L
f
±±±-f
..v 4. L;
LJ
L,4
t.
F
4
•
t11
—
..L1V
1T-.IEiI
±ILii i_Li L±LH±
Ot
L
P
6
2
(22
S
_
t
2
U
MathlO9O.004
Exam 01, Page 5 of 7
22 February 2013
(b) Label each corner point of the feasible region and write the system of equations
that corresponds to each corner point.
Point A:
—
x1
L
PointB:
ç
-x*
PointC:
S
I
L
(c) Solve the system of equations to find each corner point
SHOW YOUR WORK
Point A:
4
Point B:
(c)
(,i)
Point C:
(c)
(ii’!)
c
a:::
-.(j
(d) Find the maximum and minimum of the objective function P(x, y)
p(
,
2
-i
ô bjed-
=,
+y
f-con
2I I3
a
‘fz
(),—J’/z)
22 February 2013
Exam 01, Page 6 of 7
Mat h1090.004
6. Following the steps below, solve this
system of equations using
the Inverse Method
[ points]
/
(4)
(5)
(6)
9x + 5y + 3z = 1
3x + 2y + z = 1
2x + y + z 1
(a) Begin by writing the system
Matrix Form
in
5
L
(b)
:1
I
I
I
L’
iLZJ
Part 1:Finding the Inverse
LLs
Find the inverse matrix.
NO4tA±IDfl
.i-- 1
S 0
i_I
0(
(b)
11
6
H
LL
1?2
1
2
-13
oo
_?i
H
jOt
00
11
—)l
3 -zr?,
‘R rz
10
V
—I
I
0-4
F
-3
3
-2
L
O
O
O
-i
toto jo
,_
0l
3
1
I
-I
—12
—1
—3
—.—1
-
-z
S
L-i
I -41., 3 -1-12
0
El
o
1
—‘
0
-H
—+ 3-i--IZ
0
0 1
is]
___+‘
0#
3-2o9.
I
I
I
1
I
lo
12
I
—H
3 1?3+?2.
‘R
I•
1
0
1z-3 t?
0
C
I
40
o—1-
iLtisJ
0
—130
Li
Exam 01, Page 7 of 7
MathlO9O.004
22 February 2013
(c) Check your work to be sure you have the correct inverse matrix.
SHOW YOUR WORK
r6s
Z
1
3
n
—(
IIt
[21
4 —I
0
I
S
7
—9t9
Sk3
3
s-
—*.-
1
O
0
0
(
Part 2:Using the Inverse
(d) Use the inverse matrix you just found to solve the original system.
x=
r
-
-ir
°
-t
1
3
ri-i—)
H’ i_t*0
J L-’j
1
JL
(d)
-2-
(d)
-
(
(e) Check your work using Matrix Multiplication to show that your solution is
correct.
SHOW YOUR WORK
2
1
1rz
riio
Ok4+
1
jL
1
H]
1
V