Apply mathematical problem solving skills to a variety of problems at the college level.Examine the shape of the data’s graph and determine the type of equation to be used in the paper.

Applications of Linear, Quadratic or Exponential Equations

Apply mathematical problem solving skills to a variety of problems at the college level. Use what we have learned in the course and apply them to a topic of your choice. Write a short paper using the equations with the exception of chapter 5(interest/compound interest equations. The goal is to find data of interest which can be written as ordered pairs.

Examine the shape of the data’s graph and determine the type of equation to be used in the paper.

Does the greedy allocation rule maximize social welfare? Prove the claim or construct an explicit counterexample.

You can earn extra credit by typing up your solutions in LaTeX. I suggest you use Overleaf as a LaTeX editor.
• Exercise adapted from Problem 4.3:
Consider a set M of distinct items. There are n bidders, and each bidder i has a publicly
known subset Ti ⊆ M of items that it wants, and a private valuation vi for getting them. If
bidder i is awarded a set Si of items at a total price of p, then her utility is vixi − p, where xi is 1 if Si ⊇ Ti and 0 otherwise. Since each item can only be awarded to one bidder, a subset W of bidders can all receive their desired subsets simultaneously if and only if Ti ∩ Tj = ∅ for each distinct i, j ∈ W .
(a) Is this a single-parameter environment? Explain fully.
(b) The allocation rule that maximizes social welfare is well known to be NP hard and so we make a greedy allocation rule. Given a reported truthful bid bi from each player i, here is a greedy allocation rule:
(i) Initialize the set of winners W = ∅, and the set of remaining items X = M.
(ii) Sort and re-index the bidders so that b1 ≥ b2 ≥ · · · ≥ bn.
(iii) For i = 1, 2, 3, . . . , n :
If Ti ⊆ X, then:
– Delete Ti from X.
– Add i to W .
(iv) Return W.
Is this allocation rule monotone? If so, find a DSIC auction based on this allocation rule. Otherwise, provide an explicit counter example.
(c) Does the greedy allocation rule maximize social welfare? Prove the claim or construct
an explicit counter example.

Is the correlation you obtained in cell A13 weak, moderate or strong? State your result in cell A14.

We would like learn about the correlation coefficient using Excel. Lets look at the following question.
To find out how genetically related the cholesterol level is, they measured the cholesterol level of eight mothers and their daughters. They obtained the following data.

Mother Her daughter
157 154
189 150
201 184
174 170
159 158
213 192
149 143
143 132

Evaluate the correlation coefficient and describe the correlation.

We will now learn how to use Excel to quickly check our answers.
Open Excel
In cell A1 type Mother
In cell B1 type Her daughter
Below Mother type the data from the exam one by one with pressing Enter in between: 157,189,201,174,159,213,149,143
Below Her Daughter type the data from the exam one by one with pressing Enter in between: 154,150,184,170,158,192,143,132
In cell A11 type Correlation coefficient
In cell A13 begin typing =Cor for correlation coefficient
After you typed =Cor you will only be offered one choice =CORREL, double click on it.
Then highligh all data under Mother
type ,
Then highligh all data under Her daughter
Press Enter. you should obtain the correlation coefficient. To learn more about correlation coefficient study the textbook.

1. Is the correlation you obtained in cell A13 weak, moderate or strong? State your result in cell A14.
2. Is the correlation you obtained in cell A13 positive or negative? State your result in cell A15. Explain what it means in cell A16.

How did the members of the accounting firms violate the standards of integrity and credibility?

Regarding Enron, this was a company that resulted in the creation of the Sarbanes-Oxley Act and many reforms to the accounting profession. Research the company and answer the following questions.
How did the members of the accounting firms violate the standards of integrity and credibility?
Do you believe the new standards that resulted from the Enron scandal to be adequate?
Name and explain two aspects of the Sarbanes – Oxley Act of 2002.
Ratio Analysis. Using the 2000 Enron 10-K, calculate 2 years of the following liquidity, solvency and profitability ratios. Include your calculations and analysis for these ratios and what they tell you about the company.
Liquidity: Current ratio, Accounts receivable turnover
Solvency: Debt to assets ratio, Times interest earned
Profitability: Profit margin, Earnings per share

How many units of each model should National make each month to maximize its monthly profit?Explain your answer.

National Business Machines manufactures x model A portable printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $40 for each model A and $35 for each model B portable printer.

If the total number of portable printers demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?
Please with a link to a graph solution.

How did the members of the accounting firms violate the standards of integrity and credibility?

Regarding Enron, this was a company that resulted in the creation of the Sarbanes-Oxley Act and many reforms to the accounting profession. Research the company and answer the following questions.
How did the members of the accounting firms violate the standards of integrity and credibility?
Do you believe the new standards that resulted from the Enron scandal to be adequate?
Name and explain two aspects of the Sarbanes – Oxley Act of 2002.
Ratio Analysis. Using the 2000 Enron 10-K, calculate 2 years of the following liquidity, solvency and profitability ratios. Include your calculations and analysis for these ratios and what they tell you about the company.
Liquidity: Current ratio, Accounts receivable turnover
Solvency: Debt to assets ratio, Times interest earned
Profitability: Profit margin, Earnings per share

How many units of each model should National make each month to maximize its monthly profit?

National Business Machines manufactures x model A portable printers and y model B portable printers. Each model A costs $100 to make, and each model B costs $150. The profits are $40 for each model A and $35 for each model B portable printer.

If the total number of portable printers demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?