Estudiante

EXAM

III - VERSION

1

1. For

A
and

= [~ ~]

3-4 B=[3 o -1 5]
find the entry in the second row and third column in the product AB.

a) 11

b) -7

c)

-11

d) 7

e) 3.

2. Find

%

in the following system

+ 2y % +y -3% + Y %

2z

=5
=6 =7
e) none of the above.

5z
2z

a)

-1

b) -2

c) 2

d) 3

3. Find the entry in the second row and firstcolumn of the inverse of the matrix

011
214 [1 0 1]

a) 2

b) -2

c) 1/2

d) -1/2

e) none of the above.

37

Exam

III- Version 1

4. A set S is described by the inequalities given below. Find the y coordinate of the corner point of S in the half plane x > o. x+2~0 2x +y $ 8

3~- 5y$-1
a) 2

b) -2

c)

1

d)

S

has no corner points in the half plane x ~O.

e) None of the above 5. A Leontief input-output model has two goods, steel and oil. The production processes are such that .8 units of steel and .1 unit of oil are required to produce 1 unit of steel, and .4 units of steel and .5 units of oil are required to produce 1 unit of oil. Suppose that the economy is meeting an external demand of 2 units of steel and 1 unit of oil. Then a) The levelof production b) The level of production c) The level of production d) The level of production e) None of the above of steel is at of steel is at of steel is at of steel is at two times the level of production of oil. 4.5 times the level of production of oil. 2.5 times the level of production of oil. 3.5 times the level of production of oil.

6. The Mythic Pizza Co. makes two types of pizza: theMilano and the Romano. Each Milano pizza uses 9 oz. of dough and 14 oz. of cheese. Each Romano pizza uses 11 oz. of dough and 6 oz. of cheese. On a certain business day they have 60lbs. (960 oz.) of dough and 50 Ibs. (8000z.) of cheese available. They always wish to produce at least twice as much Romano pizza as Milano pizza. The profit on each Milano pizza is $.40. The profit on each Romanopizza is $.60. SET UP the problem of finding the largest possible profit for this business day and

show your work

38

Exam III - Version

1

7. Find the entry in the first row and second column of the product A· A for the matrix

A=[~
a) 10 b) -18
c) 19 d) 31

-;]
e) 18 .

8. A lottery winner plans to invest part of her $90,000 in utility bonds and the rest in a savings account.She wants to keep at least 1/3 of her money in utility bonds but wants to have at least twice as much money in savings as in utility bonds. Set up equations or inequalities to express her options. show your work; but do NOT solve

9. Find the entry in the second row and first column of the inverse of the matrix

-.3 .4 [.4 -.2]
a) 2

b) -2

c)

.2

d) 3

e)

-.3.

10. Supposefor tax purposes a $200,000 building is depreciated at a rate of 4 percent of its original value per year and a $500,000 per year building is depreciated at a rate of 8 percent of its original value per year. Let t represent the number of years that a building has been depreciated and V be the value of the building after t years. Write linear equations relating V and t for the two buildings. When dothe two buildings have the same value? show your work r••• -., , , - --\

G :

M If-X

• X I.

'I

6)1 Sf.J~J

c-cr;-o

\ 13

A I'lx. +-61i:>; i'O()/ j' :!f9".D J ~", If ~ ~ 'Ix. +-11

'7~ ~
])

;(r7
V

==

9~ 0 o~ )( 4

-3

0,00 0;1

,~

2.~ /

~21JO 000 _ ;> 000 £;-1 v:::.

t: ::.trr I?

5'0000 -{;) 'ICJlooo:e-) -

39

EXAM
1. Let

III - VERSIONA=
0 2 2

2

042 (1 2 3)
What is the entry in the second row and third column of A-I? (a)

-!

(b)

!

(c) -2

(d) 1

(e) none of the others

2. Find all solutions of the system of equations with the augmented matrix

(a) x = 1, Y = 1, z = 0 (c) x = 1, y = 1 - z, z arbitrary (e) none of the others

(b) x = 1, (d) x = 1,

y

= 1, z arbitrary
= 0,
z

y

=0

3....