Matt and Lisa are driving together to a shopping mall, looking forward to buying some clothes. Matt wants to stop by Sports Authority to buy the new jersey of his favorite hockey team, whereas Lisa wants to go to Banana Republic to buy a new outfit. Both find the idea of going together to both stores a little boring, so they agreed beforehand to split and go individually to their desired store. After shopping individually, they decide to meet at Applebee’s to grab some food before leaving. The Banana republic, the Sports Authority shops and the Applebee’s are located at (2, 3), (5, 5) and (1, 4), respectively. Suppose that the parking lot is located in a straight line given by the function y = 1/3x − 1. That is, customers can park in the mall as long as they do it on top of the line. 3-1. Assuming rectilinear distances, where should they park the car in order to minimize the total distance they must walk? Explain your results. 3-2. Suppose Matt is recovering from a leg injury, so they decided that Matt’s walking distance is twice as valuable as Lisa’s walking distance. Find the new optimal parking spot.

1 ____( solve_R__RStudio )

You’ve been hired as a consultant for a new planned NYC “quadrathalon”, in which participants run from Hunter’s Point South Park in Queens to Socrates Sculpture garden, take a kayak from there to Roosevelt Island, swim from there to John Jay park on Manhattan, cycle across to the Boat Basin, then swim down to a concluding party at Riverside pier 1. The organizers are worried about pollution while swimming in the two rivers. Studies have show the East River has unacceptable pollution levels a percentage of time given by p_E in the data sheet, while the Hudson river has unacceptable levels p_H of the time. Assuming these probabilities are independent answer the following:

p_E = 52   p_H = 22   p_HE = 37

1. What is the probability of having only one river contaminated? (they can move the kayak section from one river to the other).
2. What is the probability of having neither river contaminated?

You have received new information: if the East River is contaminated, the chances of the Hudson river also being contaminated goes up to p_HE (Manhattan pollutes both).   Redo the questions above using this new information.

____( solve_R__RStudio )

You’ve been hired as a consultant for a new planned NYC “quadrathalon”, in which participants run from Hunter’s Point South Park in Queens to Socrates Sculpture garden, take a kayak from there to Roosevelt Island, swim from there to John Jay park on Manhattan, cycle across to the Boat Basin, then swim down to a concluding party at Riverside pier 1. The organizers are worried about pollution while swimming in the two rivers. Studies have show the East River has unacceptable pollution levels a percentage of time given by p_E in the data sheet, while the Hudson river has unacceptable levels p_H of the time. Assuming these probabilities are independent answer the following:

p_E = 52   p_H = 22   p_HE = 37

-What is the probability of having only one river contaminated? (they can move the kayak section from one river to the other).

-What is the probability of having neither river contaminated?

You have received new information: if the East River is contaminated, the chances of the Hudson river also being contaminated goes up to p_HE (Manhattan pollutes both).   Redo the questions above using this new information.

A singer quartet consisting of Angel, Betty, Carlos and Diana wants to practice their singing. However due to the pandemic they decide to do so at a baseball park to keep social distancing. Angel stands on the home plate, Betty goes to third base, Carlos to second base and Diana to first base. While they are getting ready a bird flies along the line joining third base and home, Betty says “That bird is singing at a frequency of 350 hertz”, but Angel says “No, it is singing at 340 hertz.” Soon after the bird leaves the park Diana sings a 440 hertz note, Carlos hears it 0.1 second later and sings a 261 hertz note.

Part a

Make a drawing of the bird’s flight path along the line joining third base and home, with an arrow indicating the direction of flight, towards home or away from home.

Part b

Explain why you chose that direction, include any equations that support your explanation.

Part c

How far is Carlos from Diana? Show your calculations.

Part d

What is the period of Carlos’ note at 261 Hertz. Include your calculations

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use . Factor A is method of loading and unloading; Factor B is the type of ride.

Set up the ANOVA table (to whole number, but -value to 2 decimals and value to 1 decimal, if necessary). The p-value for Factor A is? What is your conclusion with respect to Factor A? The p-value for Factor B is? What is your conclusion with respect to Factor B? The p-value for the interaction of factors A and B is? What is your conclusion with respect to the interaction of Factors A and B? What is your recommendation to the amusement park?

You’ve been hired as a consultant for a new planned NYC “quadrathalon”, in which participants run from Hunter’s Point South Park in Queens to Socrates Sculpture garden, take a kayak from there to Roosevelt Island,  swim from there to John Jay park on Manhattan, cycle across to the Boat Basin, then swim down to a concluding party at Riverside pier 1.  The organizers are worried about pollution while swimming in the two rivers.  Studies have show the East River has unacceptable pollution levels a percentage of time given by p_E in the data sheet, while the Hudson river has unacceptable levels p_Hof the time.  Assuming these probabilities are independent answer the following:

p_E =  52  p_H =  22   p_HE = 37

1. What is the probability of having only oneriver contaminated? (they can move the kayak section from one river to the other).
2. What is the probability of having neitherriver contaminated?

You have received new information: if the East River is contaminated, the chances of the Hudson river also being contaminated goes up to p_HE(Manhattan pollutes both).   Redo the questions above using this new information.

General This case study is from the Corporate Finance book, chapter 8 in the eBook (pg. 653 in the hard copy, page 261 in eBook). The case study will require you to perform a financial analysis and make some capital investment decisions for Bethesda Mining Company. You will need to prepare various operating cash flows in order to perform your analysis and make a recommendation. The case study is also stated below. Please complete the case study using the excel template found in Engage. As a reminder, please show all of your work! You cannot receive partial credit if you do not show your work. This means that you should use formulas and link to cells whenever possible instead of typing in numbers. This reduces the risk of input errors and it also makes it easier for me to follow your work and thought process.

Case Study:

Bethesda Mining Company is a midsized coal mining company with 20 mines located in Ohio, Pennsylvania, West Virginia, and Kentucky. The company operates deep mines as well as strip mines. Most of the coal mined is sold under contract, with excess production sold on the spot market.

The coal mining industry, especially high-sulfur coal operations such as Bethesda, has been hard-hit by environmental regulations. Recently, however, a combination of increased demand for coal and new pollution reduction technologies has led to an improved market demand for high-sulfur coal. Bethesda has just been approached by Mid-Ohio Electric Company with a request to supply coal for its electric generators for the next four years. Bethesda Mining does not have enough excess capacity at its existing mines to guarantee the contract. The company is considering opening a str?p mine in Ohio on 5,000 acres of land purchased 10 years ago for $5.4 million. Based on a recent appraisal, the company feels it could receive $7.3 million on an after-tax basis if it sold the land today.

Strip mining is a process where the layers of topsoil above a coal vein are removed and the exposed coal is removed. Some time ago, the company would simply remove the cool and leave the land in an unusable condition. Changes in mining regulations now force a company to reclaim the land; that is, when the mining is completed, the land must be restored to near its original condition. The land can then be used for other purposes. As they are currently operating at full capacity, Bethesda will need to purchase additional equipment, which will cost $43 million. The equipment will be depreciated on a seven-year MACRS schedule. The contract only runs for four years. At that time the coal from the site will be entirely mined. The company feels that the equipment can be sold for 60 percent of its initial purchase price. However, Bethesda plans to open another strip mine at that time and will use the equipment at the new mine.

The contract calls for the delivery of 500,000 tons of coal per year at a price of $60 per ton. Bethesda Mining feels that coal production will be 750,000 tons, 810,000 tons, 830,000 tons, and 720,000 tons, respectively, over the next four years. The excess production will be sold in the spot market at an average of $48 per ton, Variable costs amount to $21 per ton and fixed costs are $3.7 million per year. The mine will require a net working capital investment of 5 percent of sales. The net working capital (“NWC") will be built up in the year prior to the sales.

Bethesda will be responsible for reclaiming the land at termination of the mining. This will occur in Year 5 The company uses an outside company for reclamation of all the company's strip mines. It is estimated the cost of reclamation will be $3.9 million. After the land is reclaimed, the company plans to donate the land to the state for use as a public park and recreation area as a condition to receive the necessary mining permits. This will occur in Year 5 and result in a charitable expense deduction of $7.3 million. Bethesda loss in any year will result in a tax credit. faces a 38 percent tax rate and has a 12 percent required return on new strip mine projects. Assume a loss in any year will result in a tax credit

You have been approached by the president of the company with a request to analyze the project. Calculate the payback period, profitability index, net present value, and internal rate of return for the new strip mine. Should Bethesda Mining take the contract and open the mine?

Required:

1. To analyze this project, we must calculate the incremental cash flows generated by the project. Since net working capital is built up ahead of sales, the initial cash flow depends in part on this Prepare the sales forecast in tab 1 of the excel workbook cash outflow. Therefore you need to begin your analysis by calculating your sales forecast.

2. Calculate the initial cash outflow for this project; use tab 1 to calculate your answer.

3. Use tab 2 in the excel workbook to calculate your operating cash flows for this project for years 1 through 6.

4. You will also need to calculate the net working capital cash flow each year, and the cash flow for the sale of the equipment. Calculate these amounts for this project.

5. Finally, using the net cash flows calculated above (operating cash flow, net working capital and after-tax salvage value), calculate the following for this project:

a. Payback Period

b. Profitability Index

c.IRR

d. NPV

e. recommendation (why should they accept or reject?) Explain your answer

Format grading will be required to use the Case Study Template. The template is an excel spreadsheet. Please show all your work

Lavado Rapido is a Mexican company that owns and operates a large automatic car wash facility near Mexico City. The following table provides data concerning the company’s costs:

[Fixed Cost per Month] [Cost per Car Washed]

Cleaning supplies $1.10

Electricity $1,500 $0.20

Maintenance $0.35

Wages and salaries $6,500 $0.80

Depreciation $6,000

Rent $9,500

Administrative expenses $3,500 $0.20

The company actually washed 10,000 cars in October and expected to collect an average of $5.50 per car washed. The company reported the following actual results.

Actual Results

Revenue 75,000

Cleaning Supplies 12,000

Electricity 3,000

Maintenance 4,500

Wages and salaries 16,500

Depreciation 6,000

Rent 9,500

Administrative Expenses 7,800

Required: Prepare the company’s flexible budget and variances for October.

This is all the information I was given, I wasn't given a planned wash amount.

Exercise 9-12 Activity Variances [LO9-2]

Lavage Rapide is a Canadian company that owns and operates a large automatic car wash facility near Montreal. The following table provides data concerning the company’s costs:

For example, electricity costs are $1,000 per month plus $0.10 per car washed. The company expects to wash 8,200 cars in August and to collect an average of $6.90 per car washed. The company actually washed 8,300 cars in August.

Required:

Calculate the company's activity variances for August. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.)