Math 141 Exam 2 Review
1. Set up and solve the following linear programming problem. A farmer has at most 40
acres on which to plant two crops A and B. His cultivation costs are $30 per acre of A
and $50 per acre of B. He can spend at most $1840 on cultivation. Each acre of A
requires 40 labor hours and each acre of B requires 30 labor hours. He can use at most
1450 labor hours. His profits are $400 per acre of A and $500 per acre of B. How many
acres of each should he plant to maximize his profit?
2. For the information in problem 1, write the statement "The number of acres of crop B
is to be at least 25% of the total acres planted." Does the solution change under this
additional constraint?
3. Fill in each blank with an appropriate symbol from ,  ,  ,  , 
3___{1, 2, 3, 4, 5}
{1, 2, 3, 4, 5}_____{2, 4, 6, 8}={2,4}_____{2, 4, 6, 8}
4. A, B, and C are sets in a universal set, U. Write each of the following with A, B, and
C and unions, intersections and or complements.
a) { x: x is in at least one of A, B, C }
b) { x: x is in A and B but x is not in C }
c) { x: x is in A or B but x is not in C }
5. Shade a Venn diagram for each set.
a)
(A B
C
)C
b)
A  (B
C
 C)
c)
A
C
B
C
C
C
6. U = the students at TAMU who have only one major
A = {x : x is an accounting major }
B = {x: x is a junior accounting major }
C = { x: x is a junior }
D = { x: x is a psychology major }
Which of the following use correct notation and are true?
a)
B A
b)
B  A
c)
A D  
d)
A D
C
e)
B  AC
7. Write each statement using unions, intersections and or complements.
a) the set of all accounting majors together will all psychology majors.
b) the set of all junior psychology majors.
c) the set of all juniors and all psychology majors.
d) the set of all juniors who are not psychology majors.
e) the set of all accounting majors who are not juniors.
8. 120 people were asked if they read or listen to music in their leisure time. 85 said they
read. 65 said they listen to music. 10 said they do neither. a) How many read and listen to
music? b) How many read but do not listen to music?
9. Sixty students were asked if they belong to the theatre club, the Spanish club or the art
club.
Their responses told:
3 belong to none of the clubs
13 belong to the art club only.
25 belong to the theatre club or the Spanish club but do not belong to the art club.
33 belong to exactly one of these clubs.
24 belong only to the Spanish club or only to the art club.
20 belong to exactly two of these clubs.
32 belong to the art club.
22 belong to the theatre club and possibly one other club but not all three.
Fill in a Venn diagram with the numbers in each region.
How many belong to exactly one club?
How many belong to none of the three clubs?
10. A multiple choice test has 15 questions with 1 correct answer and 3 incorrect answers
for each. How many ways can the test be answered if
a) all questions are answered?
b) exactly two questions are left blank?
c) exactly three questions are answered incorrectly?
d) exactly 10 questions are answered correctly?
11. How many 8-letter words (codes) can be made from 8 distinct letters if
a) repeats are allowed? b) no repeats are allowed? c) exactly one repeat is allowed?
12. How many ways can 12 jurors be chosen from 20 male and 30 female potential jurors
if a) no restriction is made? b) there must be an equal number of men and women?
13. Three legal cases must each be assigned one lawyer from a firm of 6 lawyers. How
many ways can this be done if a) no lawyer works on more than one case? b) any lawyer
can work any number of the cases?
14. Twenty people must choose a committee of 8 people and decide on a president, vice
president and treasurer within the 8 chosen. How many ways can this be done?
15. A coin is tossed 5 times. How many sequences of heads and tails contain exactly 2
heads?
16. How many ways can 6 couples line up so that spouses are next to each other?
17. Three presidents, 4 vice presidents, and 6 secretaries are to be in a photo. How many
ways can they be arranged in a line if people of the same rank are next to each other?
18. How many ways can a group of 5 boys and 3 girls be chosen from a group of 16 boys
and 14 girls?
19. For each experiment give two possible outcomes of the sample space, S. Give n(S)
and give n(A) for the specified event, A.
a) Toss two dice. A is the event that at least one 4 or at least one 6 occurs.
(think complements)
b) Select three marbles from a box of 15 marbles colored so there are 8 red, 4 blue and 3
yellow. A is the event that exactly one blue or exactly one yellow is chosen.
c) Choose 3 cards with replacement in sequence from a standard 52-card deck and roll a
6- sided die. A is the event that three aces are chosen and the die lands with 1 or 2 on top.
d) Choose 3 cards simultaneously from a standard 52-card deck and roll a 6-sided die. A
is the event that three aces are chosen and the die lands with 1 or 2 on top.