Get premium membership and access questions with answers, video lessons as well as revision papers.
a)The subject of calculus is an area of mathematics called the classical optimization model. It has many business and economic applications. It is concerned mainly with optimization i.e. the best combination of variables that will either maximize benefits or minimize losses. In the context of maximizing contribution, calculus is used in determining the level of production that will maximize profit or contribution. This is achieved through the concept of the rate of change in y, the dependent variable, given a change in x, the independent variable. Once a functional relationship between these two variables is established, then through the process of differentiation an optimal output level is determined.
In calculas if y = f(x), then at maximum or minimum the rate of change of „y? with respect to x will be Zero.
For instance, suppose the Revenue “R” and Quantity “Q” are relate.d by the formula:
R = 15q – ¾ q2 Then at optimal production level:
(R 3
= 15 - q = 0.
(q 2
3 15 x 2
15 = q or q = = 10
2 3
So that maximum revenue should be achieved at a production level of 10 units.
The same concept is used for minimization of costs. Suppose costs are related to the units produced as follows:
C = x2 – 10x + 200.
(C
Then = 2x – 10.
(x
(c
At minimum level, = 0, 2x – 10 = 0
(x
2x = 10
X = 5
The cost will be minimized at a production level of 5 units.
(iThe subject of calculus is an area of mathematics called the classical optimization model. It has many business and economic applications. It is concerned mainly with optimization i.e. the best combination of variables that will either maximize benefits or minimize losses. In the context of maximizing contribution, calculus is used in determining the level of production that will maximize profit or contribution. This is achieved through the concept of the rate of change in y, the dependent variable, given a change in x, the independent variable. Once a functional relationship between these two variables is established, then through the process of differentiation an optimal output level is determined.
In calculas if y = f(x), then at maximum or minimum the rate of change of „y? with respect to x will be Zero.
For instance, suppose the Revenue “R” and Quantity “Q” are related by the formula:
R = 15q – ¾ q2 Then at optimal production level:
(R 3
= 15 - q = 0.
(q 2
3 15 x 2
15 = q or q = = 10
2 3
So that maximum revenue should be achieved at a production level of 10 units.
The same concept is used for minimization of costs. Suppose costs are related to the units produced as follows:
C = x2 – 10x + 200.
(C
Then = 2x – 10.
(x
(c
At minimum level, = 0, 2x – 10 = 0
(x
2x = 10
X = 5
The cost will be minimized at a production level of 5 units.
b)i) Profit will be maximized at a sales level in which marginal Revenue = Marginal Cost.
Company A sells goods at Sh. 200 per unit to company B. The unit selling price to B is fixed at Sh. 200/=. Let “q” be the optimal sales unit.
Then the Revenue function for firm A is:
R = q x 200 = 200q.
(R And Marginal Revenue, = 200.
(q
The cost function for firm A is: C = 2q2 + 40q + 80
(R
The marginal cost is then: ( 4q ( 40
(q
(R (c At maximum profit: (
(q (q
i.e. 200 = 4q + 40 160 = 4q 40 = q.
A will maximize its profit at a weekly sale of 40 units.
Revenue function for firm B R = 1000q – 16q2.
At weekly purchase of 40 units:
R = 1000 x 40 – 16 x (40)2 R = 40,000 – 25,600
R = 14,400 per week.
Weekly cost:
C = 2q2 + 80q + 400
= 2 x (40)2 + 80 + 40 + 400
= 3,200 + 3,200 + 400
= 6,800.
Add cost of sales:
40 units @200 = 8,000 Total cost 14,800
Less Revenue 14,400
Weekly loss (400)
(ii) Company B will maximize profit if its Marginal Revenue = Marginal Cost.
Given the TR function R = 1000q – 16q2, the MR function is obtained as follows:
(R
MR = = 1000 – 32q………….. (1)
(q
Given the Total Cost, C = 2q2 + 80q + 400, the MC function is obtained as follows:
(C MC = = 4q + 80
(q
Equating the two functions and solving for q:1000 – 32q = 4q + 80.
920 = 36q 25.6 = q
q = 25 units
A weekly sales of 25 units will maximize the profit of firm B.
(iii) When the two firms merge, and in the absence of any tangible benefits to be brought by the merger, we simply add their total revenue and cost as if they were operating individually. We can then apply calculus to establish profit maximizing output and weekly profit as shown below:
Total Revenue:
From A Ltd = 200q per week
From B Ltd = 1000q – 16q2
Total R
= 1200q – 16q2
(R
(MR =
(q Total cost:
=
1200 – 32q
A Ltd
=
2q2 + 40q + 80
B Ltd
=
2q2 + 80q + 400
Total cost C =
4q2 + 120q + 480
(c
(MC = = 8q + 120
(q
(c (R At maximum (
(q (q
8q + 120 = 1200 – 32q
40q = 1080 q = 27.
Profit maximizing output = 27 units per week.
The weekly profit is established by substituting q = 27 in the profit function
P = TR – TC.
First, Total Revenue = 1200q – 136q2
= 1200 x 27 – 16 x (27)2 = 20,736
And Total Cost = 4q2 + 120q x 480
= 4 x (27)2 x 120 x 27 + 480 = 6,636
(Weekly profit 14,100
) Profit will be maximized at a sales level in which marginal Revenue = Marginal Cost.
Company A sells goods at Sh. 200 per unit to company B. The unit selling price to B is fixed at Sh. 200/=. Let “q” be the optimal sales unit.
Then the Revenue function for firm A is:
R = q x 200 = 200q.
(R And Marginal Revenue, = 200.
(q
The cost function for firm A is: C = 2q2 + 40q + 80
(R
The marginal cost is then: ( 4q ( 40
(q
(R (c At maximum profit: (
(q (q
i.e. 200 = 4q + 40 160 = 4q 40 = q.
A will maximize its profit at a weekly sale of 40 units.
Revenue function for firm B R = 1000q – 16q2.
At weekly purchase of 40 units:
R = 1000 x 40 – 16 x (40)2 R = 40,000 – 25,600
R = 14,400 per week.
Weekly cost:
C = 2q2 + 80q + 400
= 2 x (40)2 + 80 + 40 + 400
= 3,200 + 3,200 + 400
= 6,800.
Add cost of sales:
40 units @200 = 8,000 Total cost 14,800
Less Revenue 14,400
Weekly loss (400)
(ii) Company B will maximize profit if its Marginal Revenue = Marginal Cost.
Given the TR function R = 1000q – 16q2, the MR function is obtained as follows:
(R
MR = = 1000 – 32q………….. (1)
(q
Given the Total Cost, C = 2q2 + 80q + 400, the MC function is obtained as follows:
(C MC = = 4q + 80
(q
Equating the two functions and solving for q:1000 – 32q = 4q + 80.
920 = 36q 25.6 = q
q = 25 units
A weekly sales of 25 units will maximize the profit of firm B.
(iii) When the two firms merge, and in the absence of any tangible benefits to be brought by the merger, we simply add their total revenue and cost as if they were operating individually. We can then apply calculus to establish profit maximizing output and weekly profit as shown below:
Total Revenue:
From A Ltd = 200q per week
From B Ltd = 1000q – 16q2
Total R
= 1200q – 16q2
(R
(MR =
(q Total cost:
=
1200 – 32q
A Ltd
=
2q2 + 40q + 80
B Ltd
=
2q2 + 80q + 400
Total cost C =
4q2 + 120q + 480
(c
(MC = = 8q + 120
(q
(c (R At maximum (
(q (q
8q + 120 = 1200 – 32q
40q = 1080 q = 27.
Profit maximizing output = 27 units per week.
The weekly profit is established by substituting q = 27 in the profit function
P = TR – TC.
First, Total Revenue = 1200q – 136q2
= 1200 x 27 – 16 x (27)2 = 20,736
And Total Cost = 4q2 + 120q x 480
= 4 x (27)2 x 120 x 27 + 480 = 6,636
(Weekly profit 14,100
Moraa orina answered the question on April 2, 2018 at 18:13
- Describe the limitations of the CVP (Cost, Volume and Profit) Analysis(Solved)
Describe the limitations of the CVP (Cost, Volume and Profit) Analysis.
Date posted: April 1, 2018. Answers (1)
- Describe the competitive strategy by Michael Porter(Solved)
Describe the competitive strategy by Michael Porter.
Date posted: April 1, 2018. Answers (1)
- Describe the BCG matrix as used as a corporate business portfolio analysis tool(Solved)
Describe the BCG matrix as used as a corporate business portfolio analysis tool.
Date posted: April 1, 2018. Answers (1)
- Give the factors which determines the gains from international trade(Solved)
Give the factors which determines the gains from international trade.
Date posted: April 1, 2018. Answers (1)
- Describe the various gains from trade(Solved)
Describe the various gains from trade.
Date posted: April 1, 2018. Answers (1)
- Case study analysis of communication strategysummarize the communication strategy of your chosen organization, b) analyze the communication strategy of your chosen organization, and c) explain...(Solved)
In this assignment, you will need to a) summarize the communication strategy of your chosen organization, b) analyze the communication strategy of your chosen organization, and c) explain how you would integrate the communication strategy into the current organization where you work or into a former organization where you have worked.
A. Summarize the Communication Strategy
Locate an article that discusses the communication strategies used by your chosen organization. After reading your chosen article, you may find the exercise below to be helpful in developing a summary paragraph. Identify the author(s) of your chosen article, and complete the following exercise:
[Insert author’s name here] discusses how innovative communication processes have helped [insert name of the organization here] resolve [insert issue here].
The top reason [insert author’s name here] holds that position is __________.
A second reason [insert author’s name here] holds that position is __________.
A third reason [insert author’s name here] holds that position is __________.
After filling in the blanks, you should have a list of the positions and claims made by the authors about your chosen organization. Shape your notes into a summary paragraph. (Do not simply include the list that you completed in the exercise above.)
Remember that the summary paragraph is where you will present information from the source. You will provide your analysis and interpretation in the following section of the paper.
B. Analyze the Communication Strategy
Be sure to include how the communication strategy impacts the organization on multiple levels. Feel free to use the four levels of sales, services, value chain, and continuous improvement as a model, which was discussed in the case study on the Dell Computer Corporation in the Unit VI Lesson. (Note: Your categories may be different.)
In the analysis portion of the assignment, discuss any problems (or potential problems) with the communications in your chosen organization, and provide potential solutions based on your research. Include ways that effective management could help to provide a solution.
C. Explain Integration Techniques
Finally, explain how this communication strategy could be integrated into your current or former workplace.
You will need to reference at least two academic sources.
Use the standard five-paragraph format (introduction/body/conclusion). APA format should be used. The assignment should be a minimum of three pages in length. Content, organization, and grammar/mechanics will be evaluated.
Date posted: March 31, 2018. Answers (1)
-
a)Explain the following terms as used in network analysis:
i)Backward pass;
ii)Crashing; ...(Solved)
a)Explain the following terms as used in network analysis:
i)Backward pass;
ii)crashing;
iii)Slack;
iv)Earliest start times;
v)Critical-path activities;
b)XYZ Construction Company is building a 250-unit apartment complex in Embakasi, Kenya. The project consists of hundreds of activities involving excavating, framing, wiring, plastering, painting, landscaping and more. Some of the activities must be done sequentially and others can be done simultaneously. Also, some of the activities can be completed faster than normal by acquiring additional resources.
Required:
i)How would Quantitative Techniques be used to solve this problem?
ii)What would be the uncontrollable inputs?
iii)What would be the decision variables of the model? The objective function?
The constraints?
iv)Is the model deterministic or stochastic?
v)Suggest assumptions that could be made so simplify the model.
Date posted: March 31, 2018. Answers (1)
- Your firm is the auditor of Trent Textiles Ltd, and you are planning your
audit work on the stock-take, which will be carried out at...(Solved)
Your firm is the auditor of Trent Textiles Ltd, and you are planning your
audit work on the stock-take, which will be carried out at the firm‟s year-
end of 31 May 19X3.
Trent Textiles manufactures knitted garments, including pullovers. The
production process comprises:
(a) Knitting the individual components (e.g body and arms);
(b) Sewing the components together to form the finished garment;
(c) Cleaning, finishing, pressing and folding the garments;
(d) Packing the garments, ready for dispatch to the customer.
Trent Textiles does not have a perpetual inventory system, so the value of
the stock in the accounts is found from the stock-take at the year-end. For
management purposes, Trent Textiles carries out a full stock-take every
three months.
Your permanent file of the company confirms that it has a single factory
and no internal audit department.
You have been asked by the manager in charge of the audit to suggest the
work you will perform at the stages listed below.
Required:
(a) State the work you will carry out prior to the commencement of the
stock-take.
(b) State the procedures you will check during the stock-take to ensure
the company‟s staff have accurately recorded the stock.
(c) State the work you will carry out and the matters you will record at the
stock-take
Date posted: March 30, 2018. Answers (1)
- In auditing the financial statements of companies which use computerized
accounting systems, the auditors may find that this traditional (audit) trail is
often obscured. Various...(Solved)
In auditing the financial statements of companies which use computerized
accounting systems, the auditors may find that this traditional (audit) trail is
often obscured. Various techniques can be used in order to give the
auditors greater assurance when the audit trail is lost.
Required;
a) Explain why there is a possible loss of audit trail when companies
utilize computerized accounting systems and why auditing through
the computer assists the auditors in overcoming this loss of audit
trail.
b) Explain how the auditors can use analytical procedures in order to
give them greater assurance when there is a loss of audit trail.
c) Outline how audit software can be used by the auditors in order to
assist them in carrying out their analytical procedures.
d) Explain the possible reasons and implications (audit) of significant
changes in the following ratios when compared to the prior years
ratios:
i. The debtors turnover ratio has decreased over the year.
ii. The stock turnover ratio has decreased from the previous year‟s
rate.
Date posted: March 30, 2018. Answers (1)
- (a) Define tests of controls, substantive procedures and walk-through
tests.
(b) Explain how assessment of systems and controls impacts upon the
main stages of the...(Solved)
a) Define tests of controls, substantive procedures and walk-through
tests.
(b) Explain how assessment of systems and controls impacts upon the
main stages of the audit process
(c) Explain the role that internal control questionnaires and internal
control evaluation questionnaires play in determining the effectiveness
of the systems of internal control.
Date posted: March 30, 2018. Answers (1)
- What are the common characteristics of less developed countries?(Solved)
What are the common characteristics of less developed countries?
Date posted: March 29, 2018. Answers (1)
- Explain why countries engage in international trade(Solved)
Explain why countries engage in international trade.
Date posted: March 29, 2018. Answers (1)
- The following are common errors that students make when discussing supply and demand. What is the mistake in each? (i) At equilibrium, demand equals supply (ii) The quantity of...(Solved)
The following are common errors that students make when discussing supply and demand. What is the mistake in each?
(i) At equilibrium, demand equals supply.
(ii) The quantity of demand is greater than the quantity of supply
(iii) They move along the line from both ends to an equilibrium in the middle
(iv) The increase in demand causes an increase in supply
Date posted: March 27, 2018. Answers (1)
- After hurricane Andrew hit Florida and Louisiana, consumers expressed outrage at the high prices being charged for chainsaws, generators and bottled water. If government followed...(Solved)
After hurricane Andrew hit Florida and Louisiana, consumers expressed outrage at the high prices being charged for chainsaws, generators and bottled water. If government followed consumers’ demands and imposed price ceilings in these markets, what is likely to be the result?
Date posted: March 27, 2018. Answers (1)
- (The Meaning of Full Employment) When the economy is at full employment, is the unemployment rate at zero percent? Why or why not? How would...(Solved)
(The Meaning of Full Employment) When the economy is at full employment, is the unemployment rate at zero percent? Why or why not? How would a more generous unemployment insurance system affect the full employment figure?
Date posted: March 25, 2018. Answers (1)
- Write short notes on the concept of quasi-rent?(Solved)
Write short notes on the concept of quasi-rent?
Date posted: March 25, 2018. Answers (1)
- Define wages and discuss the various kinds of labour?(Solved)
Define wages and discuss the various kinds of labour?
Date posted: March 25, 2018. Answers (1)
- Define trade union.What are the main objectives of trade union?(Solved)
Define trade union.What are the main objectives of trade union?
Date posted: March 25, 2018. Answers (1)
- Discuss the factors that affect relative wages(Solved)
Discuss the factors that affect relative wages.
Date posted: March 25, 2018. Answers (1)
- Critically examine the Ricardian Theory of rent(Solved)
Critically examine the Ricardian Theory of rent
Date posted: March 25, 2018. Answers (1)