In Class Final Exam Review Math 141
1. Demand and Supply. The market will demand at most 1000 units of a certain product
even if it is free. For each decrease of $5 in the price, the demand increases by 10
units. Suppliers will provide none at a price of $200. They will provide 1600 units at
a price of $600 per unit. Find the equilibrium point.
 x
2. A    1
 3
a) Find 2 A
2

y

6 
T
2
B  
3
B
1
7
0 

 1
b) Find AB
3. A farmer plants two crops, A and B. Each acre of A uses 30 lb of seed Each acre of B
uses 25 lb of seed. Each acre of A requires 40 labor hours and each acre of B requires 30
labor hours. He plans to plant 20 acres of A and 45 acres of B.
a) Write a product of two matrices showing the total lb of seed and labor hours.
b) If labor costs $15 per hour and seed costs $5 per lb, what matrix product shows
the total cost?
4. Each augmented matrix represents a system of equations. Solve each system or state no
solution. a)
1

0

0

0
0
1
0
0
3 

2

1 

0 
b)
1

0
0
3
1
5
5. Graph the region described by x  6 ,
2

7
y  4,
c)
1

0

 0
0
1
0
5 x  4 y  40 ,
 1

2

0 
x  0,
y  0.
6. A company produces two products, A and B. Each unit of A requires 2 hours in the
parts dept., 1 hour in assembly and 1 hour in finishing. Each unit of B requires 3 hours in
the parts dept., 1 hour in assembly and 2 hours in finishing. They have available 30 hours
in parts, 13 hours in assembly and 18 hours in finishing. How many of each should they
produce to maximize profit if :
a) profits per unit of A and B are $20 and $45 respectively.
b) profits per unit of A and B are $30 for each.
c) profits per unit of A and B are $30 and $25 respectively.
7. 40 people were asked if they run, walk or swim for exercise.
A total of 20 run but 10 said they only run.
2 only swim.
6 walk and swim but do not run.
5 do all 3 types of exercise.
7 run and swim.
26 walk or swim.
How many do none of the three?
8. A builder has 10 lots on which to build 3 spec homes. How many ways can he decide
where to build if :
a) the homes are identical?
b) the homes are all different?
c) two of the homes are identical and the 3rd is different.
9. How many ways can you assign 5 new cases to some of 8 lawyers if each case needs
exactly one lawyer and
a) any lawyer can work any number of cases?
b) no lawyer works on more than one case?
10. A box contains 5 red balls and 7 blue balls and 3 yellow balls. A person randomly
selects 6 all at once.
a) Find the probability that exactly 2 red or exactly 2 blue are chosen.
b) Find the conditional probability that at exactly 2 blue are chosen given exactly 2 red
are chosen.
c) Find the probability of exactly two blue and at least one yellow.
11. A company manufactures its product on each of 3 machines. The portion produced
and the probability of a defective product for each machine is shown.
Portion of total production.
Probability of defective
Machine I
0.40
0.020
Machine II
0.25
0.025
Machine III
0.35
0.030
a) Find the probability that a randomly selected product is defective.
b) Find the probability that a product produced by machine III is defective.
c) Find the probability that a defective product was produced by machine III.
12. A box contains 4 red and 3 blue balls. A person chooses 3 all at once. X is the number
of blue balls chosen. Write the distribution of X. Find E(X) showing all work.
13. A box contains 6 red and 3 blue balls. A person chooses one at a time until he gets a
red ball. X is the number of blue balls chosen. Write the distribution of X and find E(X).
14. A stock was watched for 5 consecutive days. The price per share on each day is
shown.
Day
1
2
3
4
5
$/share
15.76 15.90 16.15 16.00 15.90
Find the mean, median, mode and standard deviation of the price per share for these 5
days.
15. A quiz was given to a group of students. The scores and frequencies are shown.
Score
0
1
2
3
4
5
# students
2
3
6
8
7
7
Find the mean, median, mode and standard deviation for the scores.
16. A box contains 8 red and 12 blue balls. A person selects 30 in succession with
replacement. (one after another, replacing each time). X is the number of times the ball is
red.
a) Find the probability that X is equal to its expected value.
b) Find P ( 9  X  15 ) .
17. Heights of American women aged 18-24 are normally distributed with mean 65.5
inches and standard deviation 2.5 inches.
Find the probability that a randomly selected woman in this age group is
a) between 63 and 67 inches.
b) at least 64 inches.
c) at most 64 inches.
Find a height so that the expected portion of women who are
d) at least this height is 0.20.
e) at most this height is 0.40.
18. A person purchases a $300,000 home putting 20% down and paying interest rate 6%
compounded monthly. The loan will be repaid in monthly installments over 30 years paid
at the end of each month.
a) How much of the first payment is interest?
b) Find their monthly payment.
c) How much do they still owe at the end of ten years?
19. A person wants to be able to withdraw $1000 per month for ten years. Interest is 4%
compounded monthly.
a) How much will they need at the beginning of the ten years?
b) If they will begin withdrawing 20 years from now, how much should they deposit to
have this amount (found in part a) in 20 years?