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BB202 Business Mathematics
Tutorial 1
- (a) Find the straight line equation that passes through (^ )^ and (^ ). (b) Find the value of when is 30.
- Solve the following simultaneous equations:
(a) and
(b) and
(c) and
- Solve the following quadratic equations
(a)
(b)
(c)
- A manufacturer sells his product at RM5 per unit
(a) What is the equation for this revenue function?
(b) What is the total revenue for sales of 5000 units of product?
(c) Fixed costs are constant at RM3000 regardless of the number of units of product involved. Total cost is equal to the sum of fixed costs and variable costs. In this company, variable cost is estimated at 40% of total revenue. Find the total cost function.
(d) What is the break-even point?
- A company invests in a particular project and it has been estimated that after months of running, the cumulative profit (in thousand RM) from the project is given by function , where represents time in months. The project can run for nine months at the most.
(a) What is the initial cost of the project?
(b) Calculate break even time points for the project.
(c) Calculate the time point when project will reach maximum profit.
(d) Calculate the maximum profit.
(e) Based on your calculation above, when is the best time to end the project?
- A general insurance company can sell 20 car insurance policies for every month if they charge RM40 per policy. Moreover, for each decrease or increase of RM1 in the price, the company can sells 1 more or less insurance policy, respectively. Fixed costs are RM100. Variable costs are RM32 per policy.
(a) What is the price function of the insurance policy?
(b) By using the price function in (a), construct the revenue function.
(c) Find the cost function of the insurance policy.
(d) By using the answers from (b) and (c), find the profit function.
(e) What is the maximum monthly profit that the company can achieve from selling the car insurance policies?
BB202 Business Mathematics
Tutorial 3
- How long does it takes a sum of money to triple itself at a simple interest rate of 5% per annum?
- Twenty-four months ago, a sum of money was invested. Now the investment is worth RM12 000. If the investment is extended for another twenty-four months, it will become RM 14 000. (a) Find the simple interest rate that was offered. (b) Find the original principal that was invested.
- On 10 March 2011 Emmy deposited in an account that paid 8% per annum simple interest. On 28 August 2011, she withdrew from the account and the balance in the account was Find the initial deposit using the Banker’s rule.
- A debt of RM 500 due two months ago and RM 900 due in nine months are to be settled by two equal payments, one at the end of three months and another at the end of six months. Find the size of the payment using (a) the present as the focal date (b) the end of six months as the focal date,
assuming money is worth 10% per annum simple interest.
- (a) Fauzi invests RM 6690 at 5% simple interest in a bank. Find the amount in the account after eight months. (b) A loan of is made on 20 April 2012 at a simple interest rate of 6% per annum. The accumulated amount on 23 December 2012 is RM 2008. Using Banker’s Rule, find (i) the term of the loan in days (ii) the value of.
- RM 9000 is invested for 7 years 3 months. This investment is offered 12% compounded monthly for the first 4 years and 12 % compounded quarterly for the rest of the period. Calculate the future value of this investment.
- Lolita saved RM 5000 in a savings account which pays 12% interest compounded monthly. Eight months later she saved another RM5000. Find the amount in the account two years after her first saving.
- How long does it takes a sum of money to double Itself at 14% compounded annually?
- Kang wishes to borrow some money to finance some business expansion. He has received two different quotes: Bank A : charges 15.2% compounded annually. Bank B : charges 14.5% compounded monthly. Which bank provides a better deal?
- Roland invested RM10 000 at 12% compounded monthly. This investment will be given to his three children when they reach 20 years old. Now his three children are 15, 16 and 19 years old respectively. If his three children will receive equal amounts, find the amount each will receive.
- Jimmy invests RM15 000 in an account for six years. The investment account pays 8% compounded semi-annually for the first two years and 9% compounded monthly for the rest of the period. (a) What is the maturity value of this investment? (b) Find the interest earned from this investment.
- A debt of RM 1000 bearing interest at 10% compounded annually is to be discharged by the sinking fund method. If four annual deposits are made into a fund which pays 7% compounded annually, (a) Find the annual interest payment. (b) Find the size of the annual deposit into the sinking fund.
BB202 Business Mathematics
Tutorial 5
- The quantity index for the number of bicycles exported by a country from 1996 to 2000, compared to 1990 are shown in the table below. Year 1996 1997 1998 1999 2000 Index 120 130 140 150 160
(a) Find the number of bicycles exported in 1990 if there were 10 million bicycles exported in 2000. (b) If the trend increase of bicycle exported is maintained, in which year will the bicycles be doubles that in 1990?
- The prices and quantities sold at a Department Store for various items for May 2000 and May 2003 are : Item 2000 Price ($)
Quantity Sold
Price ($)
Quantity Sold Ties (each) 1 1000 2 900 Suits (each)^30 100 40 Shoes (pair) 10 500 8 500
What is value index for May 2003 using May 2000 as the base period?
- The cost, in Dollars, in preparing a cup of tea sold by a shop is summarized below. 1999 2000 Weight Tea leaves 5.00^ 6.00^1 Water 0.20 0.26 3 Milk 0.10 0.15 2 Labor 1.00^ 1.20^3 (a) Find the price relative for each of the component in preparing a cup of tea in year 2000 as compared to year 1999. (b) Find the weight index number in preparing a cup of tea in year 2000 as compared to year 1999.
- Fruit prices and the amounts consumed for 2000 and 2003 are in the table below. Use year 2000 as base year. Fruit 2000 2003 Price($) Quantity Price($) Quantity Bananas (pound) 0.23 100 0.35 120 Grapefruit (each) 0.29 50 0.27 55 Apples (pound) 0.35 85 0.35 85 Strawberries (basket) 1.02 8 1.40 10 Orange (bag) 0.89 6 0.99 8
(a) Determine the simple average price index and the simple aggregate price index.
BB202 Business Mathematics
Tutorial 6
- Differentiate the following with respect to. (a) (b) ( ) (c) (^ ) (d) ( ) (e)
- Differentiate the following with respect to. (a) (^ ) (b) ( ) (c) [√ (^ )] (d) ( )^ ( )
- Differentiate the following with respect to. (a) (b) ( ) (c) (d) ( )
- Differentiate the following with respect to. (a) (^ ) (b) (^ ) (c) √ (d) (^) √
- Differentiate the following with respect to. (a) ( ) (b) (^ )^ (^ ) (c) √ (d) (e) (f) ( )
- Differentiate the following with respect to.
(a) (b) (c)
(d)
- Find ( ) for the following functions.
(a) ( ) (b) ( ) ( ) (c) ( )^ √
- Integrate each of the following.
( ) ∫ ( ) ∫
BB202 Business Mathematics
Tutorial 8 – Application of calculus
Q1 The total revenue in euro per month of a product, R ( x ) is given by R ( x ) = 40x – 0.08x^2 , where x is the number of units produced and sold per month. Find
a) R ( 50 ) b) The average revenue function c) The average revenue when 50 units are sold d) The marginal revenue function e) The marginal revenue when 50 units are sold
Q2 The weekly marginal cost function, C’ ( x ) and the weekly marginal revenue function, R’(x) of a company assembling personal computers are given as C’ ( x ) = $ ( 3x^2 – 118x+1315 ) and R’ ( x ) = $ ( 1000 – 4x ) , where x s the number of computers assembled per week. If the fixed costs are $5,000, find a) The profit function b) The increase in profit if the number of computers assembled increases from 30 to 35 per week c) The maximum profit per week d) The total revenue obtained and the price per unit when profit is maximized
Q3 The marginal cost of a product in dollars, C’ ( x ) is given by C’ ( x ) = 24-0.024x+0.006x^2 , where x is the level of output. The cost of producing 200 units is 22,700. Find a) The cost function b) The fixed cost c) The cost when 500 units are produced
Q4 The rate of sales of a new product is given by
f ( x ) = 1200 – 950e-x
where x is the number of months the product is on the market. Find the total sales during the first year.
Q
first year.
Calculatethemaximumpossiblenumberofpoliciesthecompanycansellduringthe
policieswillbesoldduringthfirstyear. 1000
newinsurancepolicy.If isspentondevelopmentand isspentonmarketing,
Aninsurancecompanyhas$160,000tospendon thedevelopmentandmarketingofa
4
3 4
1 x y
x y
BB202 Business Mathematics
Tutorial 9
- Weekly sales record (in thousand Ringgit Malaysia) for a company for September 23, 2019 through 14 October, 2019 is given below. Week Sales Sep-23 34. Sep-30 35. Oct-07 34. Oct-14 33. (a) Copy the following table below into your answer booklet and complete it by using the single parameter exponential smoothing with to forecast value for October 21, 2019.
( ) | |
1
2
3
4
5
Total
(b) Copy the following table below into your answer booklet and complete it by using the two-parameter exponential smoothing with and to forecast value for October 21, 2019.
( ) | |
1
2
3
4
5
Total
(c) Calculate the mean square error to determine which method provides the best forecast.
(d) Calculate the mean absolute deviation to determine which method provides the best forecast.
