- Conduct breakeven analysis and able to solve the supply-demand problems and applications in
revenue. - Compute interest, present and future values of annuities and calculate Perpetuity.
- Evaluate the basic differentiation and apply derivatives to solve simple business problems.
Assignment Objective - To test understanding of students on main Mathematical concepts lie under the above Los.
- Test the ability of the students to apply Mathematical concepts in business problems.
Assignment Tasks - Suppose an airline announces that its earnings this year are lower than expected due to reduced
ticket sales. The airline spokesperson gives no information on how the company plans to turn
things around, he only mentioned that the current demand curve is given by ?
2 −
1
3
? − 4? = 0
and the supply curve is given by 2? + 8? − 4?
3 = 2?
2
a. Find the equilibrium points of the airline (10 marks)
IN SEMESTER INDIVIDUAL ASSIGNMENT
Module Code: MASC 10004 Module Name: Mathematical Technique for Managers
Level: 1 Max. Marks: 100
MTM (MASC 10004) – Spring – 2020 – CW 2(Assignment 2) – QP
MEC_AMO_TEM_034_01 Page 2 of 8
b. Find the Choke price (3 marks)
c. Current owners of the airline’s stock and potential buyers of the stock would adjust their
estimates of what the value of the corporation’s stock should be. As a result, the supply curve
for the stock would increase by k for each price, (note: k is the last 3 digit from your mobile
number). The demand curve for the stock would totally change to be represent by this
equation −
3?+32
16
− ? + 50 = 0, find the following (2 marks)
i. New supplied curve
ii. Slope of demand curve - Company manufactures and sells bikes. Each bike costs M R.O to make. The company’s fixed costs
are 500 R.O. In addition, the company owners know that the price of each bike comes from the
price function ? = 60 −
1
2
?
(Note: M is the first two digit from your MEC ID after alphabetic (S or F), for example if the ID is
19F18140 take the two digit after F which are 18)
a. Find the Break-even point of the company (11 marks)
b. Find the number of bikes at maximum profit of the company (3 marks)
c. Find the maximum revenue the company earned (2 marks) - Sally took a loan of 18000 Rial from S.R Finance to purchase a TV set. If the company charges
Simple interest at L% during the first 2 years, and 10% during the rest, how much will she have to
pay after 5 years? (7 marks)
(Note: L is the last digit in your MEC ID example if the ID is 18F18146 take the last digit which is
6%. In case the last digit zero take any number from your ID) - Sandy borrowed D R.O from a bank to buy a piece of land. If the bank charges 12 1
3
% compounded
each two months, what amount will she have to pay after 2 years and half? Also find the interest
paid by her. (5 marks)
(Note: D is your MEC ID after alphabetic (S or F), for example if the ID is 19F18140 take the
number after F which is 18140)
MTM (MASC 10004) – Spring – 2020 – CW 2(Assignment 2) – QP
MEC_AMO_TEM_034_01 Page 3 of 8 - Auto loan requires payments of 300 Rial at the end of each interval for 3 years at a nominal
annual rate of 9%, compounded monthly. The present value of this loan equal 9434.04 Rial
a. At what interval the payment should be made? (10 marks)
b. Find the amount will accumulated at the end of 3 years? (3 marks) - A worker age 40 wishes to accumulate a fund for retirement by depositing $3000 at the
beginning of each half a year for 25 years. Assuming all payments are certain to be made, find
the amount he will pay, if the effective interest rate is 8% compounded annually.
(5 marks) - Find the ?
′
in simplest form using the first principle of differentiation if ? = √??2 − 5
(11 marks)
(Note: L is the last digit in your MEC ID example if the ID is 18F18146 take the last digit which
is 6. In case the last digit zero take any number from your ID) - Find the second derivative of the following function in the simplest form, show your steps
?(?) = 2ln(?
2 − 4?
3
) −
?
?
2 + 3 (12 marks)
(Note: R is the 2nd digit in your mobile number, for example if the mobile number is 94566216,
then we write R as 4, in case your 2nd digit is zero take any digit from your phone number) - The cost function for the manufacture of x number of goods by a company is
?(?) = ?√?
3 – 10?
2 + 9000. The revenue is given by ?(?) = ?? − ??5?
4−1
(Note: A is the 2nd digit in your mobile number, for example if the mobile number is 94566216,
then we write A as 4, in case your 2nd digit is zero take any digit from your phone number)
a. Find the level of output at which the cost is minimum, then find the minimum cost.
(9 marks)
b. Find the marginal Revenue. (7 marks)
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