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: Lecturer 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 Q2 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 TC Q AQ A= 2 + + 2 . What levels of output Q and advertising
expenditure A should the firms choose in order to maximize profit?
Question 2 (10 points): A firm’s production function is given by Q L K= 0.25 0.25 where L is the
quantity of labor employed and K is the quantity of capital employed. The unit price of labor is
€20 and the unit price of capital is €5. If the producer’s cost is equal to €320 find 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 + 𝑄𝑠2 𝑃 = 126 − 𝑄𝑑2
where P, QS and Qd denote the price, quantity supplied and quantity demanded, respectively.
Calculate the producer’s and consumer’s surpluses at the equilibrium point. b) An investment flow is 𝐼
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.
Making one batch of strawberry cakes takes 1 hour of an employee A’s time, and 2 hours of
employee B’s time. Making one batch of chocolate cakes takes 2 hours of employee A’s time and
1 hour of employee B’s time. Employee A works 8 hours a day and employee B works only 7 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
Express this system in matrix form and hence find the values of P1 and P2 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.
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