Apple is considering marketing one of two new smartphones for the coming holiday season: iPhone 8 and iPhone X. Estimated profits in total USD under high, medium, and low demand are as follows:

There is concern that profitability will be affected by a Google's introduction of the Pixel 2 smartphone viewed as similar to the iPhone 8. Estimated profits in total USD with and without competition are as follows:

a. Develop a decision tree for the Apple problem.

b. For planning, Apple believes there is a 0.99 probability that its competitor will produce a new smartphone similar to the iPhone 8. Given this probability of competition, the director of planning in Cupertino recommends spending the ad dollars and heavily marketing the iPhone X smartphone. Using expected value, what is your recommended decision?

c. Show a risk profile for your recommendation.

d. Use sensitivity analysis to determine what the probability of competition for iPhone 8 would have to be for you to change your recommended decision alternative.

1. **A crate with a mass of 45 kg is suspended from a massless rope that runs vertically upward over a light pulley. The other end of the rope is connected to a 35 kg crate, which lies on a tabletop. The coefficients of the kinetic friction and the static friction between the crate and the surface are 0.3 and 0.5 respectively. An applied force, F, pulls the 35 kg crate to the right.

1. In the first case, the applied force is just sufficient to keep the crates from sliding. Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale.
2. How much force would need to be applied in this first case?
3. In the second case, the 35 kg crate is sliding to the right with a constant velocity. Draw clearly labeled free-body diagrams for each crate including all forces drawn to scale.
4. How much force would need to be applied in this second case?
5. In the third case, the 35 kg crate moves to the right at a constant acceleration of 0.5 m/s². Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale. In this instance, draw the direction of acceleration next to each diagram.
6. How much force would need to be applied in the third case.

A cylinder of 10-m-high, and a cross-sectional area of 0.1 m2 , has a piston (that is free to move) assumed to have negligible mass and thickness (see Figure 1(a)). Above the piston there is a liquid that is incompressible (constant density and volume) with ρliquid = 1000 kg/m3 . Below the piston there is air at 300 K, with a volume of 0.3 m3 . Assume air is an ideal gas (Ru =8.314 J.mol-1 .K-1 ; Mair = 28.9628 g/mol) Use P0 = 101.325 kPa and g = 9.807 m/s2 Find the following: a- The mass (in kg) of the liquid in the cylinder. b- The initial pressure of the air compartment. c- The initial mass of air (in kg). d- The initial internal energy of air. Another negligible mass and thickness piston is placed on top of the cylinder (see Figure 1b) and pushed down by 0.1 m to compress the air. The process is isothermal. The liquid is incompressible (its volume and phase do not change). Calculate: e- The final volume of air. f- The final temperature of air when thermal equilibrium is obtained. g- The final pressure of air. h- Does the internal energy of air change? i- The boundary work used to lower the piston located on top of the air. j- The total heat transfer outside of the piston from the air compartment.

. A bike shop is selling a fashionable newly designed folding bike. The shop is now considering how many of them to order for the coming season. The supplier requires that orders for the bikes must be placed in quantities of 25. The cost per bike is $820, $790, $750 and $700 for an order of 25, 50, 75 and 100 respectively. The bikes will be sold for $1,200 each. Since there will be a new design for folding bikes next season and there is no spare storage space in the store, any bikes left over at the end of this season will have to be sold at a low price of $450 each to another bike shop. However, if the shop runs out of bikes during the season, it will suffer a loss of goodwill among its customers. The shop estimates this goodwill loss to $60 per customer who is not able to buy a bike. From past experience, the shop estimates that the demand for folding bikes this coming season will be 25, 50, 75 and 100 bikes with probabilities of 0.4, 0.3, 0.2 and 0.1 respectively.

(a) Construct the payoff table for the above situation.

(b) Which alternative should be chosen using each of the maximax, maximin, minimax regret, Hurwicz (take α = 0.6), equal likelihood, expected value, and expected opportunity loss criteria?

(c) Find the expected value of perfect information.

Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.

a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)

b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

Mr. John Backster, a retired executive, desires to invest a portion of his assets in rental property. He has narrowed his choices to two apartment complexes, Windy Acres and Hillcrest Apartments. The anticipated annual cash inflows from each are as follows:

Mr. is likely to hold the apartment complex of his choice for about 25 years and will use this period for decision making purposes. Either apartment can be purchased for $140,000. Mr. Backster uses risk-adjusted discount rate approach when evaluating investments. His scale is related to the coefficient of variation ( for other types of investments, he also considers other measures).

a) compute the risk-adjusted net present value for Windy Acres and Hillcrest Apartments.

b) Which investment should Mr. Backster accept if the two investments are mutually exclusive? If the investments are not mutually exclusive and no capital rationing is involved, how would your decision be affected?

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $50 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $9. Use simulation to estimate the probability the profit per unit will be less than $9. If required, round your answer to one decimal place.
   
   %

what would be the optimal asset allocation? What is the expected return on the portfolio?

Greta, an elderly investor, has a degree of risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 5.2% per year, with a SD of 20.2%. The hedge fund risk premium is estimated at 10.2% with a SD of 35.2%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta is not fully convinced by this claim.

a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

a-2. What is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Daddy Wants a Diesel or Does He?

INTRODUCTION

Rebecca shook her head and gave a loud sigh as she hung up the phone from talking with her dad.

“What is it?” her roommate Claire asked.

“Per usual, Daddy Jim wants me to use my ‘schooling,’ as he likes to call it, to help him decide whether to buy a new crew cab truck with either a diesel or a gas engine,” Rebecca replied.

“Well, maybe he will forget all about it if you just wait him out,” Claire offered.

“Oh no, you do not know him like I do. He will expect a full analysis, or I will never hear the end of it!”

“Well, maybe you will think twice before bragging to him about your examination scores in accounting after this,” Claire said.

“You got that right! I will have to get on it right after my last final, or there will be no peace over break,” Rebecca responded. THE MODELS AND ENGINES

Rebecca opened the last e-mail from her dad to find the following information he compiled about the purchase decision. Jim made it quite clear that he wanted a 4 × 4 to be able to get his boat up the steep, sandy ramp he used most frequently. His friend, Kashef, had a late-model truck that impressed Jim very much. Any truck in this class that he chose would offer standard equipment, which is a huge step up from the 2012 Scion iQ he had bought when gas surged in 2012. However, Jim was not sure whether getting the standard engine (the V6), or paying extra for the V8 or Diesel made any sense. That is where Rebecca came in.

The engine choices were a 3.6-liter V6 rated at 295 horsepower, a 3.0-liter diesel V6 rated at 240 horsepower, or a 5.7-liter V8 rated at 360 horsepower. All of the trucks were capable of pulling Jim’s boat, a 17-foot Carolina Skiff that weighed just short of 1,500 lbs. including the boat, motor, and gear.

Vehicle mileage was one issue at hand, as well as Jim’s driving habits. The V6’s Environmental Protection Agency (EPA) rating was 17 city miles per gallon (MPG) and 25 highway MPG, while the diesel was rated 21 city MPG and 29 highway MPG. The V8 was rated at 15 city MPG and 22 highway MPG. The manufacturer suggested 89 octane fuel for the V8, but Jim indicated he would use 87 octane unless engine pinging became pronounced. The manufacturer’s “Build and Price” feature indicated that the V6 came standard, but the diesel was a $4,270 option, and a V8 was a $1,250 option.

GAS AND DIESEL PRICES

In his e-mail to Rebecca, Jim said diesel usually ran $0.25 more per gallon than unleaded gas. He was not sure whether this was accurate but thought it was in the ballpark. Rebecca wondered about this, since she had never paid attention to diesel prices in her own trips to fill up. She decided to check the price differential by visiting the U.S. Energy Information Administration website. See Table for the information she found.

Without computing the averages, she noticed there was a premium for diesel compared with regular gasoline, as reported by the U.S. Energy Information Administration averages.1 Jim’s estimate of $0.25 appeared a bit high. She noted that she could obtain more specific fuel price information based on geographic location. But there was also an issue of whether the area where Jim drives was in an area requiring reformulated or conventional fuel. Because she lacked specific details and needed to get to a review session for intermediate class, Rebecca decided to use the U.S. averages.

DRIVING HABITS

Rebecca did not need an e-mail to tell her about Jim’s driving habits. He had recently commented that his current Scion iQ had topped 100,000 miles after five and a half years of ownership. He bought that car as a reaction to the spike in fuel prices in 2012 and regretted his decision ever since.

Rebecca suspected that the miles he drove per year had declined some since she and her siblings had gone off to college more than three years ago, even though they usually refused to ride in his car, because, frankly, it was embarrassing. As Rebecca graduated and went off to college and with her siblings in the Peace Corps overseas, Jim would not have to drive them around anymore, thereby reducing his mileage. Rebecca also knew that Jim and her mother would take driving vacations as they became empty nesters. She decided that Jim would continue to drive approximately 18,000 miles per year for the foreseeable future. Her best guess was that 60% of his driving was highway miles, while 40% were driven in the city.

Jim had been very thrifty throughout his life. He was a very cautious investor, even more so now that he was getting older. During Rebecca’s last trip home, he had said that he thought he could continue to earn a return on all of his investments of 3.75% per year, which was in-line with the Wall Street Journal Prime Rate. Because of his thriftiness, Jim had accumulated enough wealth to pay cash for the purchase of the new car without affecting his or Rebecca’s mom’s lifestyles.

CONCLUSION

A car horn startled Rebecca out of her automotive ruminations. She motioned to her roommate that she will be out in a minute for their well-deserved, end-of-semester dinner. Rebecca knew she would need to put her thoughts into a more usable format before heading home over break. So diesel got better mileage, but it costs more per gallon and was a large additional cost at the time of purchase. This would require more than an armchair approach. Did she have all the information she needed to perform her analysis? What approach should she use to give her dad the best information to make a decision?

QUESTIONS:

4. What might Rebecca’s solution look like?

Assumption current vehicle for 6 years and new vehicle ownership for 8 years. The given discount rate: 3.75% a year. What is the present value of saving? This is the step I'm stuck at. Please provide calculation for present value saving.

5. What recommendation should Rebecca make? How should it be presented to Jim?

Gasoline and Diesel Prices per Gallon, September 2016 to February 2017

#########################PANDAS LANGUAGE##################

#########################MATPLOT LIB#########################

# read movie.csv into a DataFrame called 'movie'
# describe the dataframe
#rename the column Runtime (Minutes) with Runtime_Minutes, and Revenue (Millions) with Revenue_Millions 

# show if any column has null value

# count total number of null vlaues in the dataframe

# print those rows which has null values

# fill null values, 

#if column is numerical than fill with means (if there is no numerical missing value in 

#data frame then don't code in this)

#if column is categorical than fill with most frequent value (if there is no categorical missing value in 

#data frame then don't code in this)

# plot histogram of the column name year in movie dataframe, which shows how many movies release in a year.

# print the movie detail with title 'Grumpier Old Men'.

# show those movies which are released after 1995-01-01

# sort the movie DataFrame in decending order based on release_date

# for each year, display the total number of movie with specific gerne for example Action=1000,adventure=400

# plot histogram the upper calculated total count

​# filter the movies with specific gerne # like show only those movies which are selected Action gerne 

# filter the movies with specific gerne

# like show only those movies which are selected Action gerne

# for each Director, display all the movies with detail.

​

# count the movies and plot barchart top 10 director's movies.

​# for each Actor, display all the movies with detail.

​# count the movies and visualize the top 10 actor's movies in plot

​

In [27]:

data file