Let A={0,1,2}. R={(0,0),(0,1),(0,2),(1,1),(1,2),(2,2)} and S={(0,0),(1,1),(2,2)} be two relations on A. 1.Show that R is a partial order relation

2.Is R a total order relation?

3.Show that S is an equivalence relation.

2.Is R a total order relation?

3.Show that S is an equivalence relation.

The advertising alternatives for a company include television, radio, and newspaper advertisements. The costs and estimates for audience coverage are given in the table below:

TV newspaper radio

Cost per advertisement $2000 $600 $300

Audience/advertisemet $100,000 $40,000$18,000

The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

(a) Formulate the problem above in mathematical model.

(b) Formulate the problem in standard form.

(c) Solve this business problem using the Simplex method.

TV newspaper radio

Cost per advertisement $2000 $600 $300

Audience/advertisemet $100,000 $40,000$18,000

The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

(a) Formulate the problem above in mathematical model.

(b) Formulate the problem in standard form.

(c) Solve this business problem using the Simplex method.

Orders for clothing to cater for the coming festive season must be placed a month earlier. The cost per unit for a new fashion dress is RM30 while the anticipated selling price is RM60. Dresses that are not sold during the festive season can be sold for RM25 to a discount store. Demand is projected to be 60, 70, or 80 units. There is 50% chance that the demand will be 60 units, a 30% chance that the demand is 70 units, and a 20% chance that the demand will be 80 units.

i. Draw a payoff table.

ii. If the company decides to use the expected monetary criterion (EMV), how many units should be ordered.

iii. Use the data and construct an expected opportunity loss (EOL) table. Determine the best alternative.

i. Draw a payoff table.

ii. If the company decides to use the expected monetary criterion (EMV), how many units should be ordered.

iii. Use the data and construct an expected opportunity loss (EOL) table. Determine the best alternative.

Solve graphically and check your answer algebraically.

X – Y = 2

2X + Y = 2

7X – 5Y = 6

X – Y = 2

2X + Y = 2

7X – 5Y = 6

A manufacturer of microcomputer produces three different models. The following table summarizes wholesale process, material cost per unit and labor cost per unit. Annual fixed costs are $ 25 million.

Microcomputer

Model 1

Model 2

Model 3

Wholesale price per unit

$500

$1,000

$1,500

Material cost per unit

$175

$400

$750

Labor cost per unit

$100

$150

$225

Determine a joint total revenue function for sale of the three different microcomputer models?

Determine an annual total cost function for manufacturing the three models.

Determine the profit function for sales of the three models.

What is an annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models?

Microcomputer

Model 1

Model 2

Model 3

Wholesale price per unit

$500

$1,000

$1,500

Material cost per unit

$175

$400

$750

Labor cost per unit

$100

$150

$225

Determine a joint total revenue function for sale of the three different microcomputer models?

Determine an annual total cost function for manufacturing the three models.

Determine the profit function for sales of the three models.

What is an annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models?

Essay format

Read text A and B and then write an argumentative essay of approximately 500 words in which you discuss the role of social media in the 21st century.

Your essay should discuss both the advantages and disadvantages social media in our generation so as to present a balanced argument.

Text A

Social media - the trendsetter!

Social media have revolutionized the world, especially how we communicate and share information. More importantly, they are instantaneous!

Text B

Social media - the bad and ugly!

Findings from international studies on both youth and adults a like, continue to characterize the penetration of social media in recent times as toxic. Researchers argue that social media has given strength to and is a breeding ground for bullying, intimidation, harassment - negative behavior that affects our everyday lives directly. And in some cases, this rampant cyber - bullying has caused reputations damage and fatalities around the globe.

Read text A and B and then write an argumentative essay of approximately 500 words in which you discuss the role of social media in the 21st century.

Your essay should discuss both the advantages and disadvantages social media in our generation so as to present a balanced argument.

Text A

Social media - the trendsetter!

Social media have revolutionized the world, especially how we communicate and share information. More importantly, they are instantaneous!

Text B

Social media - the bad and ugly!

Findings from international studies on both youth and adults a like, continue to characterize the penetration of social media in recent times as toxic. Researchers argue that social media has given strength to and is a breeding ground for bullying, intimidation, harassment - negative behavior that affects our everyday lives directly. And in some cases, this rampant cyber - bullying has caused reputations damage and fatalities around the globe.

Solutions of Basic erosion and profit shifting (BEPS) problems in Third world countries;

Assess the impact of G20 and OECD BEPS project of 2013 - 2015 on the Tax Administration of Tanzania.

HINTS

1. With supported evidences from literature explores the core issues of the BEPS Project

2. evaluate the existence and validity of those issues mentioned in no 1 above on the tax administration of third world countries especially Tanzania.

3.Explain to what extent the G20 and OECD has resolved the BEPS problem

4. explore to what extent the resolutions provided by G20 and OECD of the issues of aggressive tax planning can be applicable in third world countries

HINTS

1. With supported evidences from literature explores the core issues of the BEPS Project

2. evaluate the existence and validity of those issues mentioned in no 1 above on the tax administration of third world countries especially Tanzania.

3.Explain to what extent the G20 and OECD has resolved the BEPS problem

4. explore to what extent the resolutions provided by G20 and OECD of the issues of aggressive tax planning can be applicable in third world countries

:How can a company overcome the problem of gathering internal data for research purposes when it is usually scattered widely across the organization? Do you think that Customer Relationship management (CRM) can solve this problem? If yes then how?