A small juice company spends $1200 per day on business expenses plus$1.10 per bottle ofjuice they make. They charge $2.50 for each bottle of juice they produce. How many bottles of juice must the company sell in one day in order to equal its daily costs?

Focal length and angular velocity A cylindrical container, partially filled with mercury, is rotated about its axis so that the angular speed of each cross section is $\omega$ radians/second. From physics, the function $f$, whose graph generates the inside surface of the mercury (see the figure), is given by

$$f(x)=\frac{1}{64} \omega^2 x^2+k,$$

where $k$ is a constant. Determine the angular speed $\omega$ that will result in a focal length of $2$ feet.

Liquid nitrogen, which is used in many physics research labs, can present a safety hazard if a large quantity evaporates in a confined space. The resulting nitrogen gas reduces the oxygen concentration, creating the risk of asphyxiation. Suppose $1.00 \mathrm{~L}$ of liquid nitrogen $\left(\rho=808 \mathrm{~kg} / \mathrm{m}^3\right)$ evaporates and comes into equilibrium with the air at $21.0^{\circ} \mathrm{C}$ and $101 \mathrm{kPa}$. How much volume will it occupy?

Hansus Enterprises is a start-up small business specializing in software systems for machine based high-school student tutoring in science and math. Sheryl Hansus, the owner, has spoken with lenders to obtain a loan of $50,000 now (year 0), and the same amount in years 3 and 6. Two different repayment schedules are available. They are: Schedule A: Pay a uniform amount of$19,500 in years 3 through 12. Schedule B: Pay a uniform amount of $20,000 in years 1 through 6, with “balloon” payments of an additional$20,000 in year 2 and a final amount of $40,000 in year 7. To assist in the decision of which schedule to select, determine the following: (a) Total amount repaid for each schedule. Which is smaller? (b) The equivalent annual worth of the loan amounts and of the repayments at i = 5% per year over a 12-year evaluation period. Which schedule has the smaller loss per year? Why is this the case?

You work for the Plains State Bank as an analyst specializing in the financial statements of small businesses seeking loans from the bank. Digit Retail Enterprises Inc. provides you with its balance sheet for December 31, 2012 and 2013 (Exhibit 6.21), and its income statement for 2013 (Exhibit 6.22). Digit Retail Enterprises, Inc., acquired no new property, plant, and equipment during the year.

$$\begin{array}{lcc} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ &&\textbf{31, 2013}&\textbf{31, 2012}\\ \text{ASSETS}\\ \textbf{Current Assets}\\ \text{Cash}&&\$ 50,000&\$ 36,000\\ \text{Accounts Receivable}&&38,000&23,000\\ \text{Notes Receivable}&&—&7,500\\ \text{Interest Receivable}&&—&100\\ \text{Merchandise Inventory}&&65,000&48,000\\ \text{Prepaid Insurance}&&12,000&9,000\\ \text{Prepaid Rent}&&—&\underline{2,000}\\ \quad\text{Total Current Assets}&&\underline{\$165,000}&\underline{\$125,600}\\ \textbf{Property, Plant, and Equipment}&&&\\ \text{At Cost}&&\$ 90,000&\$100,000\\ \text{Less Accumulated Depreciation}&&\underline{(35,000)}&\underline{(20,000)}\\ \text{Net}&&\underline{\$ 55,000}&\underline{\$ 80,000}\\ \quad\text{Total Assets}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \\ \text{LIABILITIES AND SHAREHOLDER’S EQUITY}\\ \textbf{Current Liabilities}\\ \text{Accounts Payable—Merchandise Suppliers}&&\$ 20,000&\$ 18,000\\ \text{Salaries Payable}&&2,800&2,100\\ \text{Rent Payable}&&3,000&—\\ \text{Advances from Customers}&&6,100&8,500\\ \text{Note Payable}&&5,500&—\\ \text{Dividends Payable}&&2,600&4,200\\ \text{Other Current Liabilities}&&\underline{3,700}&\underline{1,300}\\ \quad\text{Total Current Liabilities}&&\underline{\$ 43,700}&\underline{\$ 34,100}\\ \textbf{Shareholders’ Equity}&&&\\ \text{Common Stock}&&\$164,500&\$160,000\\ \text{Retained Earnings}&&11,800&11,500\\ \text{Total Shareholders’ Equity}&&\underline{\$176,300}&\underline{\$171,500}\\ \text{Total Liabilities and Shareholders' Equity}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \end{array}$$

$$\begin{array}{lr} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ \text{Sales Revenue}&\$270,000\\ \text{Gain on Sale of Property, Plant, and Equipment}&3,200\\ \text{Interest Revenue}&\underline{200}\\ \quad\text{Total Revenues}&\underline{\$273,400}\\ \textbf{Less Expenses:}&\\ \text{Cost of Goods Sold}&\$145,000\\ \text{Salaries Expense}&68,000\\ \text{Rent Expense}&12,000\\ \text{Insurance Expense}&5,000\\ \text{Depreciation Expense}&20,000\\ \text{Other Expenses}&\underline{13,800}\\ \quad\text{Total Expenses}&\underline{\$263,800}\\ \text{Net Income}&\underline{\underline{\$ 9,600}}\\ \end{array}$$

g. Calculate the amount of dividends paid during 2013.

Add.

$$\small \frac{3}{4} +\small \frac{1}{8}$$

The Large Hadron Collider. In 2012, the Large Hadron Collider confirmed the existence of the Higgs boson with a mass of 125 GeV. Research this particle and its discovery: Why is the Higgs boson so interesting to physicists? What is its role in the standard model of particle physics? Why are some physicists a little disappointed that the Higgs particle appears to be almost exactly what they expected? An upgraded Large Hadron Collider was turned on in 2015. Has it made any further discoveries?

Add.

$$\small \frac{3}{8} +\small \frac{1}{4} +\small \frac{1}{4}$$

Complete the problem.

$$\begin{array}{|c| c c c c c c c |c|}\hline \small \textbf{Total} &\small \textbf{(Selling Price per Share} & \times & \small\textbf{Number of Shares} & - & \small\textbf{Commission)}& =& \small\textbf{Net Sale} &\small \textbf{Amount of}\\ \small\textbf{Paid} & & & & & & & &\small\textbf{Profit or Loss}\\ \hline \$380 & (\small \$2 \frac{1}{2} & \times & 200) & - & \$26.45 &=& ? & ?\\ \hline \end{array}$$

Anna's Yogurt Shop is classic example of a small business. The shop has one location, one cash register, and one owner. The shop's floor plan is typical of businesses in this market. The yogurt machines are located just behind a glass enclosed counter containing an assortment of toppings. Customers place their orders at the right side of the counter, drift to their left to make their topping selections, and check out at the left end of the counter. In most cases, a single employee serves a customer from order to check out.

A basic principle for preventing fraud is to segregate the duties of custody, authority, and reporting. No one employee should be responsible for two or more of these duties. At Anna's Yogurt Shop, employees have access to (custody) the yogurt and toppings and sell (authority) these items to customers.

Owner Anna Sue Preston is fully aware that this lack of segregation of duties places her business at risk. Employees are very familiar with the pricing of the shop's limited menu. Rather than using the cash register, employees could calculate the total sales amount in their head. The money taken from the customer could go in the employee's pocket rather than the cash register. This type of fraud is known as skimming. Despite this risk, Anna Sue believes that the one-on-one service provided by her employees enhances the friendly atmosphere that has made her shop a local landmark.

Anna Sue contracts with a local janitorial service to clean the store each morning. Unknown to shop employees, the janitorial service has also been instructed to measure the amount of yogurt in the machines. The daily difference in the starting and ending ounces of yogurt indicates how much yogurt was actually sold. For example, selling ten small cones should use 60 ounces of yogurt.

Anna Sue has asked you to perform an analysis to determine if any of her employees are skimming sales. She has provided you with data for the past four months. The data include the quantity sales of each menu item, the names of the two employees working that day, and the actual ounces of yogurt used as determined by the janitorial service. As a result of product spills a 2.0% difference between the actual and expected ounces of yogurt used is considered acceptable.

INSTRUCTIONS

The Tableau workbook FA_CH04. Contains two charts that compare the actual and expected ounces of yogurt used. Read the caption above each chart to gain an understanding of the data presented. Use the charts to answer the following questions:

2. Examine the Average worksheet. How does your analysis of this chart change your conclusions based on the Totals worksheet?

If the mass of a spring $m_z$ is not negligible but is small com- pared to the mass $m$ of the object suspended from it, the pe- riod of motion is $T=2\pi\sqrt{\left(m+m_s/3\right)/k}$. Derive this result. (Hint: The condition $m_s \ll m$ is equivalent to the assumption that the spring stretches proportionally along its length.) (See H. L. Armstrong, $\it{American~ Journal~ of~ Physics}$, Vol. $37$, $1969$, p. $447$, for a complete solution of the general case.)

Betty owns a small store. The store has been losing money for some time. Because she is the sole owner of the business, her personal assets are at risk. Explain to Betty the differences among Chapters 7, 11 , and 13 bankruptcies. Which type of bankruptcy would you recommend and why?

Elite Service Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum, the company has combined the jobs of cashier and bookkeeper. As a result, Steve Evans handles all cash receipts, keeps the accounting records, and prepares the monthly bank reconciliations.

The balance per the bank statement on March 31, 2014, was $5,931.51. Outstanding checks were: No. 206 for$358.53, No. 441 for $292, No. 590 for$283.00, No. 781 for $286.00, No. 782 for$319.47, and No. 783 for $303.14. Included with the statement was a credit memorandum of$175 indicating the collection of a note receivable for Elite Service Company by the bank on March 21. This memorandum has not been recorded by Elite Service.

The company’s ledger showed one cash account with a balance of $6,889.53. The balance included undeposited cash on hand. Because of the lack of internal controls, Steve took for personal use all of the undeposited receipts in excess of$1,591.63. He then prepared the following bank reconciliation in an effort to conceal his theft of cash.

$$\begin{array}{lrr} \text{Cash balance per books, March 31}&&\text{\$\hspace{1pt}6,889.53}\\ \text{Add: Outstanding checks}\\ \qquad\text{No. 781}&\text{\$\hspace{1pt}286.00}\\ \qquad\text{No. 782}&\text{319.47}\\ \qquad\text{No. 783}&\underline{\text{\hspace{5pt}303.14}}&\underline{\text{\hspace{16pt}808.61}}\\ &&\text{7,698.14}\\ \text{Less: Undeposited receipts}&&\underline{\text{\hspace{8pt}1,591.63}}\\ \text{Unadjusted balance per bank, March 31}&&\text{6,106.51}\\ \text{Less: Bank credit memorandum}&&\underline{\text{\hspace{16pt}175.00}}\\ \text{Cash balance per bank statement, March 31}&&\underline{\underline{\text{\$\hspace{1pt}5,931.51 }}}\\ \end{array}$$

Instructions

(c) What principles of internal control were violated in this case?

Find the total paid.

$$\begin{array}{|c| c c c c c c c c c|} \hline \small\textbf{Company} & \small\textbf{(Number of Shares} & \times & \small\textbf{Cost per Share} & = & \small\textbf{Cost of Stock)} & + & \small\textbf{Commission} & = & \small\textbf{Total Paid}\\ \hline \text{ICN Br} & (500 & \times & \small \$73 \frac{1}{4} & = & ?) & + & \$318.00 &=& ?\\ \hline \end{array}$$