A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit, and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity; but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production, and, at the same time, payments from customers were often delayed until the product was shipped. Unable to deliver on orders, the company became so strapped for cash that employee paychecks began to bounce. Finally, out of cash, the company ceased operations entirely 3 years later.

What are some of the actions that a small company like The Grandmother Calendar Company can take if it finds itself in a situation in which growth in sales outstrips production capacity and available financial resources? What other options (besides expansion of capacity) are available to a company when orders exceed capacity?

What kind of survey (mail, telephone, interview, web, direct observation) would you recommend that a small laundry and dry cleaning business use for each of the following purposes, and why?

To estimate the proportion of residents in the same zip code who spend more than $\$20$ a month on dry cleaning.

A study reported in the Journal of Small Business Management concluded that selfemployed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1–5 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18–90, is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow.

$$\begin{matrix} \text{Lawyer} & \text{Physical Therapist} & \text{Cabinetmaker} & \text{Systems Analyst}\\ \hline \text{44} & \text{55} & \text{54} & \text{44}\\ \text{42} & \text{78} & \text{65} & \text{73}\\ \text{74} & \text{80} & \text{79} & \text{71}\\ \text{42} & \text{86} & \text{69} & \text{60}\\ \text{53} & \text{60} & \text{79} & \text{64}\\ \text{50} & \text{59} & \text{64} & \text{66}\\ \text{45} & \text{62} & \text{59} & \text{41}\\ \text{48} & \text{52} & \text{78} & \text{55}\\ \text{64} & \text{55} & \text{84} & \text{76}\\ \text{38} & \text{50} & \text{60} & \text{62}\\ \end{matrix}$$

At the $\alpha =$ .05 level of significance, test for any difference in the job satisfaction among the four professions.

In physics, it is established that the acceleration due to gravity, g $\left(in\ \mathrm{m} / \mathrm{sec}^{2}\right),$ at a height h meters above sea level is given by $g(h)=\frac{3.99 \times 10^{14}}{\left(6.374 \times 10^{6}+h\right)^{2}}$ where $6.374 \times 10^{6}$ is the radius of Earth in meters. Solve g(h)=0. How do you interpret your answer?

A business school conducted a survey of companies in its state. They mailed a questionnaire to 200 small companies, 200 medium-sized companies, and 200 large companies. The rate of nonresponse is important in deciding how reliable survey results are. Here are the data on response to this survey:

Draw a bar chart to compare the nonresponse percents for the three size categories.

How does Einstein's explanation account for each of these characteristics of the photoelectric effect? a. The photoelectric current is zero for frequencies below some threshold. b. The photoelectric current increases with increasing light intensity. c. The photoelectric current is independent of $\Delta V$ for $\Delta V \geq 1 \mathrm{V}$. d. The photoelectric current decreases slowly as $\Delta V$ becomes more negative. e. The stopping potential is independent of the light intensity. Which of these cannot be explained by classical physics? Explain.

Solve. Find the cost per mile to the nearest cent.

$$\begin{array}{|c c c c c c c c c c c|} \hline \small\textbf{(Total Daily Cost}& + & \small\textbf{Total Mileage Cost} & +& \small\textbf{Gasoline Cost} & = & \small\textbf{Total Cost)} & \div & \small\textbf{Miles} & = & \small\textbf{Cost per}\\ & & & & & & & &\small\textbf{Driven} & & \small\textbf{Mile}\\ \hline (\$160.00 & + & \$94.00 & + & \$23.89 & = & ?) & \div & 500 & = & ? \\ \hline \end{array}$$

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.)

In physics it is shown that the height s of a ball thrown straight up with an initial speed of 96 ft sec from a rooftop 112 feet high is $s=s(t)=-16 t^{2}+96 t+112$ where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground. What is the average speed of the ball from t = 0 to t = 2?

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?

Add.

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

A single firm in a perfectly competitive market is relatively small compared to the rest of the market. What does this mean? How “small” is “small”?

After completing his Certified Financial Planner designation (CFP), Andre was excited about the prospects of working with small business owners and their employees regarding retirement planning. Andre wanted to show the value of an annuity program as one of the viable investment options in a salary reduction retirement plan. In addition, he wanted to demonstrate the substantial tax benefits that annuities can provide. For instance, qualified annuities (by definition) not only reduce your current taxable salary, they also accumulate earnings on a tax-deferred basis-meaning you don't pay taxes on the earnings until they are withdrawn. Andre was developing a spreadsheet to show the way that annuities could grow using various rates of return.

Using the same information from Exercise earlier and assuming a $25 \%$ tax bracket, what would be the net effect of investing at $8 \%$ for $20$ years if taxes on the earnings were paid from the investment fund each year? How would this compare if no taxes had to be paid, such as in a tax-deferred annuity at $8 \%$ for $20$ years?