Final Test 2021-2022 Sem 1 - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Mai Nguyệt
THE INTERNATIONAL UNIVERSITY (IU) –
VIETNAM NATIONAL UNIVERSITY HCMC –
FINAL EXAM
Date: 22/01/2022
Duration: 120 minutes
Student ID:…………………………………… Name……………………………..
SUBJECT: Math for Business (BA282IU 4 credits) –
School of Business Administration
Signature:
Full name:
Lecturer
Signature:
Full name:
Mrs. Nguyen Phuong Anh (PhD)
Mr. Vu Tuan Anh (MSc)
Mr. Le Ngoc Anh Khoa (MSc)
GENERAL INSTRUCTIONS
1. This is an open book exam (textbook hardcopy, A4 handwritten notes, paper dictionary, draft
papers are allowed)
2. No talking, no material transfer during the exam
3. No mobile phone/laptop/desktop use during the exam
4. Calculator is allowed
5. Students sign and submit the scanned exam papers (with handwriting)
The Final exam includes only WRITING questions:
Question 1 (10 points): A firm s demand curve is described by
QAP 2240 −+=
where
A
is
expenditure on advertising,
P
is the price of its product and
Q
is the quantity demanded. Total
costs of production are given by
22
AAQQTC ++=
. What levels of output Q and advertising
expenditure A should the firms choose in order to maximize profit?
Question 2 (10 points):
25.025.0
KLQ =
where
L
is the
quantity of labor employed and
is the quantity of capital employed. The unit price of labor is
unit is equal to the maximum
level of production of the firm.
Question 3 (20 points):
a) The supply and demand functions of a good are given by:
𝑃 = 30 + 𝑄
𝑠
2
𝑃 = 126 − 𝑄
𝑑
2
where , and denote the price, quantity supplied and quantity demanded, respectively. P Q
S
Q
d
b)
An investment flow is 𝐼
(
𝑡
)
= 700
√
𝑡 where t is measured in years. Calculate the total
capital formation during the first three years.
Question 4 (20 points):
You are the owner of a bakery that sells two types of small cakes: strawberry and chocolate.
M
hours a day.
Every day, you need to produce at least 1 batch of strawberry cakes. You also have enough
chocolate to make at most 4 batches of chocolate cakes every day.
One batch of strawberry and chocolate cakes sells at $37 and $55, respectively. It costs $30 and
$45 to make a batch of strawberry and chocolate cakes, respectively. Your cakes are so good that
all cakes can be sold.
Determine the number of batches of strawberry cakes, and the number of batches of chocolate
cakes produced per day to maximize daily profit.
Question 5 (10 points):
Suppose David is the owner of a start-up hamburger store. After 3 days of Grand Opening, David
had received £59. This table below is the tracking of the 3-day sales.
Chicken Burger
Beef Burger
Cheeseburger
Total Revenue
Day 1
1
2
3
£11
Day 2
2
4
5
£21
Day 3
3
5
6
£27
However, the one problem is that David forgot all the price of those types of burgers.
Therefore, use the to find out the price of each type of burgers. Cramer’s rule
Question 6 (20 points):
a) The equilibrium prices P1 and P2 for two goods satisfy the equations:
9P1 + P2 = 51
3P1 + 4P2 = 39
using inverse matrix.
b) If the market extends to 3 goods with prices P1, P2, and P3 which satisfy:
P1 + 2P2 + 3P3 = 42
2P1 + P2 + 4P3 = 47
P1 + 3P2 + 4P3 = 57
Determine the equilibrium prices of three interdependent commodities using inverse matrix.
Question 7 (10 points):
Maricopa's Success scholarship fund receives a gift of $65,000. The money is invested in stocks,
bonds, and saving deposits. Stocks pay 8.3% interest, bonds pay 5.1% interest, and saving deposits
pay 3.75% interest. Maricopa Success invests $15,000 less in bonds than in saving deposits. If the
annual income from the investments is $3550, in each account? how much was invested
Note: use matrix to solve this problem.
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THE INTERNATIONAL UNIVERSITY (IU) –
VIETNAM NATIONAL UNIVERSITY HCMC – FINAL EXAM Date: 22/01/2022 Duration: 120 minutes
Student ID:…………………………………… Name……………………………..
SUBJECT: Math for Business (BA282IU 4 credits) –
School of Business Administration Lecturer Signature: Signature: Full name: Full name: Mrs. Nguyen Phuong Anh (PhD) Mr. Vu Tuan Anh (MSc) Mr. Le Ngoc Anh Khoa (MSc) GENERAL INSTRUCTIONS
1. This is an open book exam (textbook hardcopy, A4 handwritten notes, paper dictionary, draft papers are allowed)
2. No talking, no material transfer during the exam
3. No mobile phone/laptop/desktop use during the exam 4. Calculator is allowed
5. Students sign and submit the scanned exam papers (with handwriting)
The Final exam includes only WRITING questions:
Question 1 (10 points): A firm s demand curve is described by P = 40 + 2A − Q 2 where A is
expenditure on advertising, P is the price of its product and Q is the quantity demanded. Total
costs of production are given by 2 2
TC = Q + AQ + A . What levels of output Q and advertising
expenditure A should the firms choose in order to maximize profit? 2 . 0 5 . 0
Question 2 (10 points): 25 Q = L K where L is the
quantity of labor employed and K is the quantity of capital employed. The unit price of labor is unit is equal to the maximum
level of production of the firm.
Question 3 (20 points):
a) The supply and demand functions of a good are given by: 𝑃 = 30 + 𝑄2𝑠 𝑃 = 126 − 𝑄2𝑑
where P, QS and Qd denote the price, quantity supplied and quantity demanded, respectively.
b) An investment flow is 𝐼(𝑡) = 700√𝑡 where t is measured in years. Calculate the total
capital formation during the first three years.
Question 4 (20 points):
You are the owner of a bakery that sells two types of small cakes: strawberry and chocolate. M hours a day.
Every day, you need to produce at least 1 batch of strawberry cakes. You also have enough
chocolate to make at most 4 batches of chocolate cakes every day.
One batch of strawberry and chocolate cakes sells at $37 and $55, respectively. It costs $30 and
$45 to make a batch of strawberry and chocolate cakes, respectively. Your cakes are so good that all cakes can be sold.
Determine the number of batches of strawberry cakes, and the number of batches of chocolate
cakes produced per day to maximize daily profit.
Question 5 (10 points):
Suppose David is the owner of a start-up hamburger store. After 3 days of Grand Opening, David
had received £59. This table below is the tracking of the 3-day sales. Chicken Burger Beef Burger Cheeseburger Total Revenue Day 1 1 2 3 £11 Day 2 2 4 5 £21 Day 3 3 5 6 £27
However, the one problem is that David forgot all the price of those types of burgers.
Therefore, use the Cramer’s rule to find out the price of each type of burgers.
Question 6 (20 points):
a) The equilibrium prices P1 and P2 for two goods satisfy the equations: 9P1 + P2 = 51 3P1 + 4P2 = 39 using inverse matrix.
b) If the market extends to 3 goods with prices P1, P2, and P3 which satisfy: P1 + 2P2 + 3P3 = 42 2P1 + P2 + 4P3 = 47 P1 + 3P2 + 4P3 = 57
Determine the equilibrium prices of three interdependent commodities using inverse matrix.
Question 7 (10 points):
Maricopa's Success scholarship fund receives a gift of $65,000. The money is invested in stocks,
bonds, and saving deposits. Stocks pay 8.3% interest, bonds pay 5.1% interest, and saving deposits
pay 3.75% interest. Maricopa Success invests $15,000 less in bonds than in saving deposits. If the
annual income from the investments is $3550, how much was invested in each account?
Note: use matrix to solve this problem.
-------------THE END-------------