Final: 24-2-2017
Final: 15-2-2017
ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD
(Department of Mathematics)
WARNING
1.
PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2. SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Business Mathematics (1429/5405)
Semester: Spring 2017
Level: B.A, B.Com, BBA
Total Marks: 100
Pass Marks: 40
ASSIGNMENT No. 1
(Units 1-4)
All questions carry equal marks.
Q. 1 In 1987, the U.S. Census Bureau estimated that 9.1 million children under age of
five required primary child care because of employed mothers.
Type of Children Care
Number of Children
In another home
3,239,600
Day care/nursery school
2,239,600
Child cares for self
18,200
Mother cares for child at week
890,900
Care in child’s home
2,72,900
Other
91,000
Table indicates the child care alternatives and the Census Bureau’s estimates of the
number of children using each type. If a child from this group is selected at
random, what is the probability that (a) the child is cared for in his home or her
home, (b) the child is cared for himself or herself and (c) the child is cared for at
work by the mother?
Q. 2 (a)
(b)
What is the probability of drawing three cards, without replacement, from a
deck of cards and getting three kings?
The director of public works for a New England city has checked the city
records to determine the number of major snowstorms which have occurred
in each of the last 60 years. The table given below presents a frequency
distribution summarizing the findings.
Number of storms
Frequency
0
3
1
5
2
10
3
13
4
8
5
16
6
5
=60
1
a.
b.
c.
Construct the probability distribution for this study.
Draw a histogram for this distribution.
What is the probability that there will be more than two major storms in a
given year?
Q. 3 (a)
A student takes a true-false examination which consists of 10 questions. The
student knows nothing about the subject and chooses answers at random.
Assuming independence between questions and probability of .9 of
answering any question correctly, what is the probability that the student will
pass the test (assume that passing means getting seven or more correct)? If
the test contains 20 questions, does the probability of passing change (14 or
more correct)?
Solve the quadratic equation using quadratic formula.
x2 – 2x = –5
(b)
Q. 4 (a)
(b)
Solve the second degree inequality.
x2 + 4x –12 ≤ 0
Solve the inequality.
2x  9 ≥ 5
Q. 5 (a)
A dietitian is considering three food types to be served at a meal. She is
particularly concerned with the amount of one vitamin provided at this meal.
One ounce of food 1 provides 8 milligrams of the vitamin; an ounce of food
2 provides 24 milligrams; and, an ounce of food 3 provides 16 milligrams.
The minimum daily requirement (MDR) for the vitamin is 120 milligrams.
i. If xj equals the number of ounces of food type j served at the meal,
determine the equation which ensures that the meal satisfies the MDR
exactly.
ii. If only one of the three food types is to be included in the meal, how
much would have to be served (in each of the three possible cases) to
satisfy the MDR?
(b)
C=5/9 F –100/9 is an equation relating temperature in Celsius units to
temperature measured on the Fahrenheit scale. Let C=degree Celsius and
F=degree Fahrenheit; assume the equation is graphed with C measured on the
vertical axis.
i. Identify the slop and C intercept.
ii. Interpret the meaning of the slop and C intercept for purpose of
converting from Fahrenheit to Celsius temperatures.
iii. Solve the equation for F and rework parts ‘a’ and ‘b’ if F is plotted on the
vertical axis.
2
ASSIGNMENT No. 2
(Units 5-9)
Total Marks: 100
Pass Marks: 40
All questions carry equal marks.
Q. 1 (a)
b.
Find the matrix of co-factors of the matrix.
The solution to a system of equation having the form AX=B can be found by
the matrix multiplication:
 2  3 17 
 
X  
  1 2 10 
What was the original system of equations? What is the solution set?
Q. 2 The figure given below is a network diagram which illustrates the route structure
for a small commuter airline which services four cities. Using this figure, construct
an adjacency matrix. Square the adjacency matrix and verbally summarize the onestop service which exists between all cities.
Q. 3 A ball is dropped from height from the roof of a building which is 256 feet high.
The height of the ball is described by the function.
H = f(t) = –16t2 + 256
Where h equals the height in feet and t equals time measured in seconds from when
the ball was dropped.
(a) What is the average velocity during the time interval 1 ≤ t ≤ 2?
3
(b)
(c)
Q. 4 (a)
(b)
What is the instantaneous velocity at t = 3?
What is the velocity of the ball at the instant it hits the ground?
Determine the derivative of ‘f’ using the limit approach, and also determine
the slope at x = 1 and x = –2, for f(x)=x2 –3x + 5.
For the function given below determine the location of all critical points and
determine their nature.
f(x)=x3/3 –5x2 + 16x + 10
Q. 5 A community which is located in a resort area is trying to decide on the parking fee
to charge at the town-owned beach. There are other beaches in the area, and there is
competition for bathers among the different beaches. The town has determined the
following function which expresses the average number of cars per day q as a
function of the parking fee p stated in cents.
Q = 6,000 – 12p
(a)
(b)
(c)
Determine the fee which should be changed to maximize daily beach
revenues.
What is the maximum daily beach revenue expected to be?
How many cars are expected on an average day?
_____[ ]_____
4