The following data pertain to the Waikiki Sands Hotel for the month of March.

$$\begin{array}{lcc} & \textbf{ Flexible Budget March } & \textbf{ Actual Results March } \\ & \textbf{ (in thousands)* } & \textbf{ (in thousands)* } \\ \text{ Banquets and Catering } & \$ 650 & \$ 658 \\ \text{ Restaurants } & 1,800 & 1,794 \\ \text{ Kitchen staff wages } & (85) & (86) \\ \text{ Food } & (690) & (690) \\ \text{ Paper products } & (125) & (122) \\ \text{ Variable overhead } & (75) & (78) \\ \text{ Fixed overhead } & (90) & (93) \end{array}$$

$^*$Numbers without parentheses denote profit; numbers with parentheses denote expenses.

Prepare a March performance report. The report should have six numerical columns with headings analogous. Your performance report should cover only the Food and Beverage Department and the Kitchen. Draw arrows to show the relationships between the numbers in the report. For the year-to-date columns in your report, use the previous data given. You will need to update those figures using the March data given above.

A freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at $25.0^{\circ} \mathrm{C}$ to 1.80 kg of ice at $-5.0^{\circ} C$ in one hour. (a) What amount of heat must be removed from the water at $25.0^{\circ} C$ to convert it to ice at $-5.0^{\circ} C$? (b) How much electrical energy is consumed by the freezer during this hour? (c) How much wasted heat is delivered to the room in which the freezer sits?

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

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.

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.

Seven performers A, B, C, D, E, F, and G are to appear in a fund raiser. The order of performance is determined by random selection. Find the probability that

$$\textbf{a.}\hspace{10pt}\text{D will perform first.}$$

$$\textbf{b.}\hspace{10pt}\text{E will perform sixth and B will perform last.}$$

$$\textbf{c.}\hspace{10pt}\text{The comedians will perform in the following order:C, D, B, A, G, F, E.}$$

$$\textbf{d.}\hspace{10pt}\text{CF or G will perform first.}$$

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.

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.

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.

In 2012, the New York Yankees won 95 games and spent $\$ 198$ million on salaries for their players (USA Today). Is there a relationship between salary and team performance in Major League Baseball? For the 2012 season, a linear model fit to the number of Wins (out of 162 regular season games) from the team Salary $(\$ M)$ for the 30 teams in the league is:

$$\widehat{\text { Wins }}=76.45+0.046 \text { Salary. }$$

c) What does the slope mean in this context?

Determine the optimal control signal u for the system $\dot{\mathbf{x}}=\mathbf{A x}+\mathbf{B} u$ defined by

$$\mathbf{A}=\left[\begin{array}{rr}{0} & {1} \\ {0} & {-1}\end{array}\right], \quad \mathbf{B}=\left[\begin{array}{l}{0} \\ {1}\end{array}\right]$$

. Where such that the following performance index is minimized: $J=\int_{0}^{\infty}\left(\mathbf{x}^{T} \mathbf{x}+u^{2}\right) d t$

For the cycle of earlier problem, investigate the effects on cycle performance as the higher extraction pressure takes on other values. The operating conditions for the open feed. water 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.

Katie and Kim are attending a theater performance. Katie's seat is at floor level. She looks down at an angle of 18$^{\circ}$ to see the orchestra pit. Kim's seat is in the balcony directly above Katie. Kim looks down at an angle of 42$^{\circ}$ to see the pit. The horizontal distance from Katie's seat to the pit is 46ft. What is the vertical distance between Katie's seat and Kim's seat? Round to the nearest inch.

As shown in figure, an air conditioner operating at steady state maintains a dwelling at $70^{\circ} \mathrm{F}$ on a day when the outside temperature is $90^{\circ} \mathrm{F}$. If the rate of heat transfer into the dwelling through the walls and roof is $30,000\ \mathrm{Btu} / \mathrm{h}$, might a net power input to the air conditioner compressor of 3 hp be sufficient? If yes, determine the coefficient of performance. If no, determine the minimum theoretical power input, in hp.