In an effort to improve student performance, teachers at $12$ city schools are being asked to work a longer day next year for a relatively small increase in salary. For working an additional $190 \mathrm{~h}$, a teacher currently earning $\$ 79,400$ per year would see his or her salary increase to $\$ 83,500$ per year.

From the information given above, find the hourly rate the teachers will be paid for the extra hours they will work.

Suppose that a soccer goalie has a save percentage of $85 \%$ this season. In a particular game, the opposing team takes 7 shots and she stops all 7 from going in the goal. The goalie is praised by her coach, but could her good performance be attributed to random chance? Describe how to simulate this situation using the methods of this chapter. Conduct at least 20 trials of your simulation and use the results to explain whether the praise was deserved.

Cell Design produces cell phone covers for all makes and models of cell phones. Cell Design sells 1,050,000 units each year at a price of $10 per unit and a contribution margin of 40%.

A survey of Cell Design customers over the past 12 months indicates that customers were very satisfied with the products but a disturbing number of customers were disappointed because the products they purchased did not fit their phones. They then had to hassle with returns and replacements.

Cell Design’s managers want to modify their production processes to develop products that more closely match Cell Design’s specifications because the quality control in place to prevent ill-fitting products from reaching customers is not working very well.

The current costs of quality are as follows:

$$\begin{array}{lr} \text{Prevention costs}& \$210,000\\ \text{Appraisal costs}& \$100,000\\ \text{Internal failure costs}&\\ \quad\text{Rework}& \$420,000\\ \quad\text{Scrap}& \$ 21,000\\ \text{External failure costs}&\\ \quad\text{Product replacements}& \$315,000\\ \quad\text{Lost sales from customer returns}& \$787,500\\ \text{The QC manager and controller have forecast the following}& \\ \quad\text{additional costs to modify the production process.}&\\ \text{CAD design improvement}& \$150,000\\ \text{Improve machine calibration to specifications}& \$137,500\\ \end{array}$$

1. Which cost of quality category are managers focusing on? Why?

2. If the improvements result in a 60% decrease in customer replacement cost and a 70% decrease in customer returns, what is the impact on the overall COQ and the company’s operating income? What should Cell Design do? Explain.

3. Calculate prevention, appraisal, internal failure, and external failure costs as a percentage of total quality costs and as a percentage of sales before and after the change in the production process. Comment briefly on your results.

An axial fan $2 \mathrm{~m}$ in diameter is used in a wind tunnel as shown (test section $1.2 \mathrm{~m}$ in diameter; test section velocity of $60 \mathrm{~m} / \mathrm{s}$ ). The rotational speed of the fan is $1800 \mathrm{rpm}$. Assume the density of the air is constant at $1.2 \mathrm{~kg} / \mathrm{m}^3$. There are negligible losses in the tunnel. The performance curve of the fan is identical to that shown in the mentioned figure. Compute the power needed to operate the fan.

Indicate whether each of the following statements concerning anabolic steroid use is true or false.

a. Illegal anabolic steroid use has very little effect on the performance of female athletes.

b. Use of illegal anabolic steroids affects the male reproductive system.

c. Structurally, testosterone and “Andro” contain the same number of carbon atoms.

d. Structurally, testosterone and THG differ in that all steroid ring attachments are different.

Consider a Carnot-cycle heat pump with R22 as the working fluid; Heat is rejected from the R-22 at 100 F: during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 30 F. a. Show the cycle on a T-diagram. b. Find the quality of the R-22 at the beginning and end of the isothermal heat addition process at 30 F. c. Determine the coefficient of performance for the cycle.

Refrigerant 134 a enters the compressor of a vapor compression heat pump at $30 \mathrm{lbf} /$ in. $^2, 20^{\circ} \mathrm{F}$ and is compressed adiabatically to $200\ \mathrm{lbf} / \mathrm{in}^2, 160^{\circ} \mathrm{F}$. Liquid enters the expansion valve at $200\ \mathrm{lbf} / \mathrm{in}^2, 120^{\circ} \mathrm{F}$. At the valve exit, the pressure is $30 \mathrm{lbf/in.}^2$ Find

(a) the isentropic compressor efficiency.

(b) the coefficient of performance.

Suppose that you have n values to put into an empty binary search tree.

1. In how many different orders can you add the n values to the tree? This is not the same as the number of possible binary search trees for n values. Explain why.
2. What is the probability that a randomly constructed binary search tree has worst-case performance? Hint: Compute the fraction of the total number of possible orders that results in the worst case.

A windows air conditioner that consumes of 1 kW of electricity when running and has a coefficient of performance of 3 is placed in the middle of a room and is plugged in. The rate of cooling or heating this air conditioner will provide to the air in the room when running is (a) 3 kJ/s, cooling (b) 1 kJ/s, cooling (c) 0.33 kJ/s, heating (d) 1 kJ/s, heating (e) 3 kJ/s, heating

An office building requires a heat transfer rate of $20\ \mathrm{kW}$ to maintain the inside temperature at $21^{\circ} \mathrm{C}$ when the outside temperature is $0^{\circ} \mathrm{C}$. A vapor-compression heat pump with Refrigerant $22\mathrm{a}$ as the working fluid is to be used to provide the necessary heating. The compressor operates adiabatically with an isentropic efficiency of $82 \%$. Specify appropriate evaporator and condenser pressures of a cycle for this purpose assuming $\Delta T_{\text {cond }}=\Delta T_{\text {cvap }}=10^{\circ} \mathrm{C}$, as shown in figure. The states are numbered as in figure. The refrigerant exits the evaporator as saturated vapor and exits the condenser as saturated liquid at the respective pressures. Determine the (a) mass flow rate of refrigerant, in $\mathrm{kg} / \mathrm{s}$. (b) compressor power, in $\mathrm{kW}$. (c) coefficient of performance and compare with the coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the inside and outside temperatures, respectively.. Compare the results with those of previous problem and discuss.

For the cycle of Problem, investigate the effects on cycle performance as the higher extraction pressure takes on other values. The operating conditions for the open feedwater heater are unchanged from those in earlier problem. Assume that condensate drains from the closed feedwater heater as saturated liquid at the higher extraction pressure. Also feedwater leaves the heater at $12\ \mathrm{MPa}$ and a temperature equal to the saturation temperature at the extraction pressure. Construct suitable plots and discuss.

Plant acquisitions for selected companies are presented below. **1.** Natchez Industries Inc. acquired land, buildings, and equipment from a bankrupt company, Vivace Co., for a lump-sum price of $680,000. At the time of purchase, Vivace’s assets had the following book and appraisal values. $$ \begin{array}{lrr} & \textbf{Book Values} & \textbf{Appraisal Values}\\ \\ \text{Land} & \$200,000 & \$150,000\\ \text{Buildings} & 230,000 & 350,000\\ \text{Equipment} & 300,000 & 300,000\\ \end{array} $$ To be conservative, the company decided to take the lower of the two values for each asset acquired. The following entry was made. |Land|150,000|| |--|--:|--:| |Buildings| 230,000|| |Equipment| 300,000|| |$\quad$Cash||680,000| **2.** Arawak Enterprises purchased store equipment by making a $2,000 cash down payment and signing a 1-year,$23,000, 10% note payable. The purchase was recorded as follows. |Equipment|27,300|| |--|--:|--:| |$\quad$Cash||2,000| |$\quad$Notes Payable||23,000| |$\quad$Interest Payable||2,300| **3.** Ace Company purchased office equipment for $20,000, terms 2/10, n/30. Because the company intended to take the discount, it made no entry until it paid for the acquisition. The entry was: |Equipment|20,000|| |--|--:|--:| |$    $Cash||19,600| |$    $Purchase Discounts||400| **4.** Paunee Inc. recently received at zero cost land from the Village of Cardassia as an inducement to locate its business in the Village. The appraised value of the land is$27,000. The company made no entry to record the land because it had no cost basis. **5.** Mohegan Company built a warehouse for $600,000. It could have purchased the building for$740,000. The controller made the following entry. |Buildings|740,000|| |--|--:|--:| |$\quad$Cash||600,000| |$\quad$Profit on Construction||140,000| **Instructions** Prepare the entry that should have been made at the date of each acquisition.

In the 2008 baseball season, first baseman Ryan Howard of the Philadelphia Phillies led the Major Leagues with 48 home runs (HR) and 146 runs batted in (RBI). Overall, using all players with at least 300 plate appearances, the mean number of HR was $14.9$ with a standard deviation of $9.8$, whereas the mean number of RBI was $62.5$ with a standard deviation of $25.5$. Which was the more impressive PERFORMANCE? Explain, using the methods of this chapter.

A window air conditioner that consumes 1 kW of electricity when running and has a coefficient of performance of 3 is placed in the middle of a room, and is plugged in. The rate of cooling or heating this air conditioner will provide to the air in the room when running is (a) 3 kJ/s, cooling (b) 1 kJ/s, cooling (c) 0.33 kJ/s, heating (d) 1 kJ/s, heating (e) 3 kJ/s, heating