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Various tutorials on business mathematics, covering topics such as simultaneous equations, revenue functions, profit functions, interest rates, compound interest, and price indexes. It includes exercises and problems related to these topics, providing a comprehensive resource for students studying business mathematics.
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BB202 Business Mathematics
Tutorial 1
(a) and
(b) and
(c) and
(a)
(b)
(c)
(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) 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) 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
assuming money is worth 10% per annum simple interest.
BB202 Business Mathematics
Tutorial 5
(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?
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?
(a) Determine the simple average price index and the simple aggregate price index.
BB202 Business Mathematics
Tutorial 6
(a) (b) (c)
(d)
(a) ( ) (b) ( ) ( ) (c) ( )^ √
( ) ∫ ( ) ∫
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
( ) | |
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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
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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.