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M

ATH 106 QUIZ 3

N

AME: _____ __________
_______

P

rofessor: Dr. Katiraie

INSTRUCTIONS

· The quiz is worth 100 points. There are 10 problems (each worth 10 points).

· This quiz is
open book
and
open notes
,
unlimited time
. This means that you may refer to your textbook, notes, and online classroom materials, but
you may not consult anyone
. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our course schedule of the syllabus.

·
You must show your work to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor.
Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. Be sure to include your name in the document.

Consult the Additional Information portion of the online Syllabus for options regarding the submission of your quiz. If you have any questions, please contact me by e-mail (

farajollah.katiraie@faculty.umuc.edu

).

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A company that manufactures laser printers for computers has monthly fixed costs of $316,000 and variable costs of $550 per unit produced. The company sells the printers for $1,350 per unit. How many printers must be sold each month for the company to break even?

Hint: Let x represent the number of laser printers. Set up the cost function, and the revenue function. Then set cost function equal to revenue function, and solve for x.

1) _______

A) 195 printers per month

B) 395 printers per month

C) 495 printers per month

D) 295 printers per month

E) none of the above

2) A performance center has 2,900 seats. Tickets for an event are $9 and $12 per seat. Assuming that all tickets are sold and bring in a total of

$40

,500, how many of each type of ticket were sold? Set up a system of equations, and solve by augmented matrix methods using Gauss-Jordan elimination.

Hint: Please see example 1 in section 4.2

2) _______

A) 1,400 $12 seats and 2,500 $9 seats

B) 1,400 $9 seats and 2,500 $12 seats

C) 1,700 $9 seats and 1,200 $12 seats

D) 2,000 $9 seats and 900 $12 seats

E) None of the above

3) If $8,000 is to be invested, part at 12% and the rest at 7%, how much should be invested at each rate so that the total annual return will be $770? Set up a system of linear equations, letting x1 represent the amount invested at 12% and x2 the amount invested at 7%. DO NOT SOLVE THE system.

Hint: Please see examples in section 4.2. Also, note 12% = 0.12, and 7% = 0.07

3) _________

A)
0.12X1
+
0.07X2
=
770

X1
+
X2
=
8,000

B)
X1
+
X2
=
770

0.12X1
+
7X2
=
8,000

C)
X1
+
X2
=
770

0.013X1
+
0.54X2
=
8,000

D)
X1
+
X2
=
8000

0.12X1
+
0.07X2
=
9800

E)
None of the above

4) Labor and material costs for manufacturing each of three types of products, M, N, and P, are given in the table:

PRODUCT

$30

M	N	P
LABOR	$60		$30	$80
MATERIALS	$40	$70

The weekly allocation for labor is $60,000 and for materials is $90,000. There are to be 2 times as many units of product M manufactured as units of product P. How many of each type of product would be manufactured each week to use exactly each of the weekly allocations? Set up a system of linear equations, letting X1, X2, and X3 represent the number of units of products M, N, and P, respectively, manufactured in one week. DO NOT SOLVE THE SYSTEM.
Hint: Please see examples in section 4.2

4) _________

A)
50X1
+
40X2
+
50X3
=
60,000

50X1
+
20X2
+
70X3
=
90,000

3X1 –
X3
=
0

B)
75X1
+
35X2
+
50X3
=
60,000

40X1
+
40X2
+
70X3
=
90,000

X1 –
2X3
=
0

C)
50X1
+
40X2
+
50X3
=
60,000

60X1
+
40X2
+
70X3
=
90,000

X1 –
3X3
=
0

D)
60X1
+
30X2
+
80X3
=
60,000

30X1
+
40X2
+
70X3
=
90,000

X1 –
2X3
=
0

E)
None of the above

5) Solve the following by augmented matrix methods using Gauss-Jordan elimination:

5) _______

X1
– 2X2
=
1

-2X1
+
5X2
=
2

Hint: Please see example 1 in section 4.2

A) X1 = 4 AND X2 = 9

B) X1 = 9 AND X2 = 4

C) X1 = 3 AND X2 = 12

D) X1 = 12 AND X2 = 3

E) None of the above

6) Solve the following

2 1 0

1 -2 -5

æö

ç÷

èø

by augmented matrix methods using Gauss-Jordan elimination

Hint: Please see example 1 in section 4.2

6) _______

A) x = -9 AND y =9

B) x = -1 AND y =2

C) x = 3 AND y = -4

D) x = -3 AND y =4

E) None of the above

7) Solve by augmented matrix methods using Gauss-Jordan elimination:

X1 – 3X2 = -5

-3X1 – X2= 5

7) _______

Hint: Please see example 2 in section 4.2

A) X1 = 2; X2 = -5

B) X1 = -2; X2 = 1

C) X1 = -1; X2 = 2

D) X1 = -2; X2 = 0

E) None of the above

8) Solve by augmented matrix methods using Gauss-Jordan elimination:

2X1 – 3X2 = -8

5X1 + 3X2= 1

8) _______

Hint: Please see example 2 in section 4.2

A) X1 = 2; X2 = -5

B) X1 = -2; X2 = 1

C) X1 = -1; X2 = 2

D) X1 = -2; X2 = 0

E) None of the above

9) Find the coordinates of the corner points of the solution region for:

6X
+
3Y

£

24
3X
+
6Y

£

30

X

³
0

Y

³
0
Hint: Please see example 2 in section 5.2.

9) _______
A) (0,18), (21,25), (12,10)
B) (18,0), (25,0), (10,12), (0,0)
C) (11,10), (21,0), (14,11)
D) (0,0), (0,5), (4,0), and (2,4)
E) None of the above
10) Find the coordinates of the corner points of the solution region for:
3X
+
Y

£

21
X
+
Y

£

9
X
+
3Y

£

21

X

³
0

Y

³
0
Hint: Please see example 2 in section 5.2.

10) _______
A) (0,0), (0,7), (3,6), (6,3) and (7,0)
B) (18,0), (25,0), (10,12), (0,0)
C) (11,10), (21,0), (14,11)
D) (0,0), (0,5), (4,0), and (2,4)
E) None of the above
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