Sandy's Rock and Gravel Company wants to shift a mountain of gravel, estimated at about 20000 tons, from one side of their yard to the other. For this they intend to use a power shovel to fill a hopper, which in turn feeds a belt conveyor. The latter then transports the gravel to the new location. The shovel scoops up large amounts of gravel at first; however, as the gravel supply decreases, the handling capacity of the shovel also decreases because of the increased time required to move away from the hopper for a load and then return and dump. Roughly, then, we may estimate that the shovel's gravel handling rate is proportional to the size of the pile still to be moved, its initial rate being 10 ton/min. The conveyor, on the other hand, transports the gravel at a uniform 5 ton/min. At first the shovel will work faster than the conveyor, then slower. Hence, the storage bin will first accumulate material, then empty. (a) What will be the largest amount of gravel in the bin? (b) When will this occur? (c) When will the rates of bin input and output be equal? (d) When will the bin become empty?

In 2021, the Marion Company purchased land containing a mineral mine for $1,600,000. Additional costs of$600,000 were incurred to develop the mine. Geologists estimated that 400,000 tons of ore would be extracted.

After the ore is removed, the land will have a resale value of $100,000. To aid in the extraction, Marion built various structures and small storage buildings on the site at a cost of$150,000. These structures have a useful life of 10 years. The structures cannot be moved after the ore has beenremoved and will be left at the site. In addition, new equipment costing $80,000 was purchased and installed atthe site. Marion does not plan to move the equipment to another site, but estimates that it can be sold at auction for$4,000 after the mining project is completed.

In 2021, 50,000 tons of ore were extracted and sold. In 2022, the estimate of total tons of ore in the mine was revised from 400,000 to 487,500. During 2022, 80,000 tons were extracted.

1. Compute depletion and depreciation of the mine and the mining facilities and equipment for 2021 and 2022. Marion uses the units-of-production method to determine depreciation on mining facilities and equipment.

2. Compute the book value of the mineral mine, structures, and equipment as of December 31, 2022.

Describe the seven essential functions performed by all animals.

Camden Biotechnology began operations in September 2021. The following selected transactions relate to liabilities of the company for September 2021 through March 2022. Camden’s fiscal year ends on December 31. Its financial statements are issued in April. 2021

a. On September 5, opened checking accounts at Second Commercial Bank and negotiated a short-term line of credit of up to $15,000,000 at the bank’s prime rate (10.5% at the time). The company will pay no commitment fees.
b. On October 1, borrowed$12 million cash from Second Commercial Bank under the line of credit and issued a five-month promissory note. Interest at the prime rate of 10% was payable at maturity. Management planned to issue 10-year bonds in February to repay the note.
c. Received $2,600 of refundable deposits in December for reusable containers used to transport and store chemical-based products.
d. For the September–December period, sales on account totaled$4,100,000. The state sales tax rate is 3% and the local sales tax rate is 3%. (This is a summary journal entry for the many individual sales transactions for the period.)
e. Recorded the adjusting entry for accrued interest.

2022 f. In March, paid the entire amount of the note on its March 1 due date, using proceeds from a February issuance of $10 million of 10-year bonds at face value, along with other available cash.
g. The storage containers covered by refundable deposits are expected to be returned during the first nine months of the year. Half of the containers were returned in March 2022.

1. Prepare the appropriate journal entries for items a-g.
2. Prepare the current and long-term liability sections of the December 31, 2021, balance sheet. Trade accounts payable on that date were$252,000.

The capital investment committee of Ellis Transport and Storage Inc. is considering two investment projects. The estimated income from operations and net cash flows from each investment are as follows:

$$\begin{array}{lcccc} {\text{}}&\hspace{30pt}\textbf{\underline{\hspace{30pt}Warehouse\hspace{30pt}}}\hspace{0pt}&\textbf{\underline{\hspace{10pt}Tracking Technology\hspace{10pt}}}\\ \end{array}$$

$$\begin{array}{ccccc} {\text{}}&\textbf{Income from}&\textbf{Net Cash}&\textbf{Income from}&\textbf{Net Cash}\\ {\textbf{Year}}&\textbf{Operations}&\textbf{Flow}&\textbf{Operations}&\textbf{Flow}\\\hline \text{1}&\text{\$\hspace{10pt}61,400}&\text{\$\hspace{5pt}135,000}&\text{\$\hspace{10pt}34,400}&\text{\$\hspace{10pt}108,000}\\ \text{2}&\text{\hspace{15pt}51,400}&\text{\hspace{10pt}125,000}&\text{\hspace{15pt}34,400}&\text{\hspace{15pt}108,000}\\ \text{3}&\text{\hspace{15pt}36,400}&\text{\hspace{10pt}110,000}&\text{\hspace{15pt}34,400}&\text{\hspace{15pt}108,000}\\ \text{4}&\text{\hspace{15pt}26,400}&\text{\hspace{10pt}100,000}&\text{\hspace{15pt}34,400}&\text{\hspace{15pt}108,000}\\ \text{5}&\underline{\text{\hspace{15pt}(3,600)}}&\underline{\text{\hspace{15pt}70,000}}&\underline{\text{\hspace{15pt}34,400}}&\underline{\text{\hspace{15pt}108,000}}\\ &\text{\underline{\underline{\$\hspace{5pt}172,000}}}&\text{\underline{\underline{\$\hspace{5pt}540,000}}}&\text{\underline{\underline{\$\hspace{5pt}172,000}}}&\text{\underline{\underline{\$\hspace{10pt}540,000}}}\\ \end{array}$$

Each project requires an investment of $368,000. Straight-line depreciation will be used, and no residual value is expected. The committee has selected a rate of 15% for purposes of the net present value analysis.

Instructions

1. Compute the following: a. The average rate of return for each investment. Round to one decimal place. b. The net present value for each investment. Use the present value of$1 table appearing in this chapter.
2. Prepare a brief report for the capital investment committee, advising it on the relative merits of the two projects.

Climate change could have a profound effect on California's water supplies. Studies of ancient trees in the Sierra Nevada have yielded valuable insight into climatic variability in California over the past several thousand years. Bristlecone pines, the oldest living trees, have rings by which the trees can be accurately dated, and some of them are 4,000 years old. Such studies confirm that California's climate over the past millennium has been extremely variable, with severe drought conditions persisting for decades to centuries.

We can now incorporate this historical record into computer forecasts of future climates based on changing levels of greenhouse gases. California's climate is "forecast" (see Issues 5 and 6 ) to become more extreme than in the recent past. Should such forecasts, or something even more severe, become the norm, such climatic extremes will critically stress the state's water storage and delivery system and may force agonizing choices between protecting aquatic ecosystems and providing the massive amounts of water consumed by industrial agriculture, commerce, and municipalities.

Urban water use in California was about 9 million acre-feet per year as of 2005. Given a population of 36 million (most Californians live in urban areas), calculate the average daily water use per person. How does this compare to the minimal human water requirement of 50,000 liters per year?

Swen’s Ski Rental rents skis, boots, and poles for $20 a day. The daily cost per set of skis is$6. It includes maintenance, storage, and overhead. Daily profits depend on daily demand for skis and the number of sets available. Swen knows that on a typical day the demand for skis is given in the table.

$$\begin{array}{|l|l|l|l|l|l|l|l|l|} \hline \text{Number of Customers } & 90 & 91 & 92 & 93 & 94 & 95 & 96 & 97 \\ \hline \text{Probability} & 0.01 & 0.10 & 0.20 & 0.20 & 0.30 & 0.10 & 0.05 & 0.01\\ \hline \end{array}$$

How many sets of skis should Swen have ready for rental to maximize his profit?

The researchers studying vitamin C in CSB in the mentioned exercise were also interested in a similar commodity called wheat soy blend (WSB). A major concern was the possibility that some of the vitamin C content would be destroyed as a result of storage and shipment of the commodity to its final destination. The researchers specially marked a collection of bags at the factory and took a sample from each of these to determine the vitamin C content. Five months later in Haiti, they found specially marked bags and took samples. The data consist of two vitamin C measures for each bag, one at the time of production in the factory and the other five months later in Haiti. The units are mg / 100 g as in the mentioned exercise. Here are the data:

Do these data provide evidence that the mean vitamin C content of all of the bags of WSB shipped to Haiti differs from the target value of 40 mg / 100 g?

A 20,000-liter storage tank was taken out of service to repair and reattach a feed line damaged in a collision with a tanker. The tank was drained and then opened several days later for a welder to enter and perform the required work. No one realized, however, that 5 liters of liquid nonane $\left(\mathrm{C}_{9} \mathrm{H}_{20}\right)$ remained in a collection sump at the bottom of the tank after the draining had been completed. a) Nonane has a lower explosive limit of 0.80 mole% and an upper explosive limit of $2.9 \text { mole } \%^{8}$ (i.e., nonane–air mixtures at 1 atm can explode when exposed to a spark or flame if the nonane mole fraction is between the two given values). Assume any liquid nonane that evaporates spreads uniformly throughout the tank. Is it possible for the average gas-phase composition in the tank to be within the explosive limits at any time? Even when the average composition falls outside those limits, why is an explosion still a possibility? (Hint: Think about that assumption.) b) Use the Antoine equation (6.1-4) to estimate the temperature at which the system would have to equilibrate in order for the gas in the tank to be at the lower explosive limit. c) Fortunately, a safety inspector examined the system before the welder began work and immediately canceled the work order. The welder was cited and fined for violating established safety procedures. One requirement was for the tank to be purged thoroughly with steam after being drained. What is the purpose of this requirement? (Why purge, and why with steam rather than air?) What other precautions should be taken to be sure that the welder is in no danger?

Methanol is added to a storage tank at a rate of 1200 kg/h and is simultaneously withdrawn at a rate $\dot{m}_{\mathrm{w}}(t)(\mathrm{kg} / \mathrm{h})$ that increases linearly with time. At t = 0 the tank contains 750 kg of the liquid and $\dot{m}_{\mathrm{w}}=750 \mathrm{kg} / \mathrm{h}$. Five hours later $\dot{m}_{\mathrm{W}}$ equals 1000 kg/h. a) Calculate an expression for $\dot{m}_{\mathrm{w}}(t)$, letting t = 0 signify the time at which $\dot{m}_{\mathrm{w}}=750 \mathrm{kg} / \mathrm{h}$, and incorporate it into a differential methanol balance, letting M…kg† be the mass of methanol in the tank at any time. b) Integrate the balance equation to obtain an expression for M…t† and check the solution two ways. For now, assume that the tank has an infinite capacity. c) Calculate how long it will take for the mass of methanol in the tank to reach its maximum value, and calculate that value. Then calculate the time it will take to empty the tank. d) Now suppose the tank volume is $3.40 \mathrm{m}^{3}$. Draw a plot of M versus t, covering the period from t = 0 to an hour after the tank is empty. Write expressions for M…t† in each time range when the function changes.

Brynn has been volunteering at the animal shelter and has decided that she would like to adopt one of the puppies. Her parents have said that before she can have a puppy, they must fence in a portion of the backyard. At the local home improvement store, her parents have determined that they can afford 360 feet of fencing materials. Brynn’s parents have agreed to let her choose how she wants to build the fence as long as she takes into consideration the trees, storage building, and deck already in the back yard. Brynn decides it will be easiest to fence in a rectangular area and remembers that the formula for finding the perimeter of a rectangle is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width. The formula P = 2l + 2w is an example of an  equation. In algebra, we use equations to determine solutions to problems. The value or values of a variable that make an equation true are the solutions to the equation. Use substitution to rewrite the formula P = 2l + 2w to represent the amount of fencing materials that Brynn’s family can afford.

Domestic Transfer and Storage is a large trucking company headquartered in the Midwest. Rapid expansion in recent years has been financed in large part by debt in a variety of forms. In preparing the financial statements for 2018, questions have arisen regarding the way certain of the liabilities are to be classified in the company’s classified balance sheet.

A meeting of several members of the accounting area is scheduled for tomorrow, April 8, 2019. You are confident that that meeting will include the topic of debt classification. You want to appear knowledgeable at the meeting, but realizing it’s been a few years since you have dealt with classification issues, you have sought out information you think relevant. Questionable liabilities at the company’s fiscal year-end (January 31, 2019) include the following:

a. $15 million of 9% commercial paper is due on July 31, 2019. Management intends to refinance the paper on a long-term basis. In early April 2019, Domestic negotiated a credit agreement with a commercial bank for up to$12 million any time during the next three years, any borrowings from which will mature two years from the date of borrowing.
b. $17 million of 11% notes were issued on June 30, 2016. The notes are due on November 30, 2019. The company has investments of$20 million classified as “available for sale.”
c. $25 million of 10% notes were due on February 28, 2019. On February 21, 2019, the company issued 30-year, 9.4% bonds in a private placement to institutional investors.
d. Recently, company management has considered reducing debt in favor of a greater proportion of equity financing.$20 million of 12% bonds mature on July 31, 2019. Discussions with underwriters, which began on January 4, 2019, resulted in a contractual arrangement on March 15 under which new common shares will be sold in July for approximately $20 million.

In order to make notes to yourself in preparation for the meeting concerning the classification of these items, you decide to discuss them with a colleague. Specifically, you want to know what portion of the debt can be excluded from classification as a current liability (that is, reported as a noncurrent liability) and why.

1. What is the appropriate classification of each liability? Develop a list of arguments in support of your view prior to the class session for which the case is assigned.
2. In class, your instructor will pair you (and everyone else) with a classmate (who also has independently developed a position). You will be given three minutes to argue your view to your partner. Your partner likewise will be given three minutes to argue his or her view to you. During these three-minute presentations, the listening partner is not permitted to speak.
3. Then after each person has had a turn attempting to convince his or her partner, the two partners will have a three-minute discussion to decide which classifications are more convincing. Arguments will be merged into a single view for each pair.
4. After the allotted time, a spokesperson for each of the four liabilities will be selected by the instructor. Each spokesperson will field arguments from the class as to the appropriate classification. The class then will discuss the merits of the classification and attempt to reach a consensus view, though a consensus is not necessary

An article in the Wall Street Journal discussed the sidewalk vegetable stands in New York City’s Chinatown. About 80 of these small vegetable stands operate along a handful of streets in that neighborhood. Most supermarkets buy vegetables from large wholesalers. In contrast, the entrepreneurs who run the stands in Chinatown buy from smaller wholesalers located in the neighborhood. These wholesalers, in turn, buy primarily from smaller family farms, some located overseas. Because these wholesalers make several deliveries per day, the owners of the stands do not have to invest in substantial storage space and the refrigerators that supermarkets use to keep vegetables fresh. The reporter compared prices for vegetables sold by these stands with vegetables sold by her supermarket: “In almost every case, Chinatown’s prices were less than half what I would pay at the supermarket. Among the bargains: broccoli for 85 cents a pound, $1 each for pomegranates, oranges for a quarter.”

Why doesn’t competition among supermarkets drive the prices of vegetables they sell down to the prices of the vegetables sold in the Chinatown stands?

The ankle-arm blood-pressure index (AAl) is defined as the ratio of ankle systolic blood pressure/arm systolic blood pressure and is used for the diagnosis of lower extremity arterial disease. A study was conducted to investigate whether the AAl can be used as a screening test for atherosclerotic diseases in general. The subjects were 446 male workers in a copper smelter in Japan. Each subject had an AAl determination as well as an electrocardiogram (ECG). From the ECG, an S-T segment depression was defined as an S-T segment $\geq$ 0.1 mV below the baseline in at least 1 of 12 leads in a resting ECG. S-T segment depression is often used as one characterization of an abnormal ECG. The data in the table below were presented relating AAl to S-T segment depression.

Association between ankle-arm bloodpressure index (AAI) and S-T segment depression

What is the PV'? (Hint: Assume that the subjects in this study are a random sample from the general population of Japan.)