MARGINAL ANALYSIS - Economics for Business Decision

You are a business owner of a firm that services trucks. A customer would like to rent a truck from you for one week, while you service his truck. You must decide whether or not to rent him a truck. You have an extra truck that you will not use for any other purpose during this week. This truck is leased for a full year from another company for $350/ week plus $.50 for every mile driven. You also have paid an annual insurance premium, which costs $70/ week to insure the truck. The truck has a full 100-gallon fuel tank. The customer has offered you $500 to rent the truck for a week. The price includes the 100 gallons of fuel that is in the tank. It also includes up to 500 miles of driving. The customer will pay $.50 for each additional mile that he drives above the 500 miles. You anticipate that the customer will bring back the truck with an empty fuel tank and will have driven more than 500 miles. You sell fuel to truckers at a retail price $3.35/gallon. Any fuel you sell or use can be replaced at a wholesale price of $2.95/gallon. The customer will rent a truck from another company if you do not accept the proposed deal. In either case, you will service his truck. You know the customer and are confident that he will pay all charges incurred under the agreement.

1. Should you accept or reject the proposed deal? Why, or why not? Show calculations.

2. Would your answer change if your fuel supplier limited the amount of fuel up to 100 gallons/ week you could purchase from him at the wholesale price? Explain.

A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years. Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2 years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will be $700 for the first year, increasing by 2% per year thereafter.

A German car will cost $45,000 and have fuel usage of 21mpg for the first 5 years, and decrease by 1% thereafter to year 8. Repair cost will start at $1000 in year 1 and increase by 4% per year. It will have a salvage value of $7000 at the end of year 8. Insurance cost will be $850 the first year, increasing by 2% per year thereafter.
The American car will cost $35,000 and have fuel usage of 20mpg for the first 3 years, and will decrease by 3% per year thereafter. Repair cost will be $800 in year 1, increasing by 4% per year thereafter. Being an American, the graduate will price the pride of owning an American car at $0.4 for every 20 miles driven, increasing by 2% per year. Insurance cost will be $800 per year increasing by 2.2% per year. The car can be sold for $5500 at the end of year 8.
If the graduate anticipates driving 150000 miles by the end of year 8 and the average interest rate is expected to remain at 5% per year, which car is economically affordable based on present worth analysis? Assume fuel cost will be $3 per gallon in year 1 and increase by an average of 2% per year. Show all your workings.

21. In a survey of women in a certain country​ (ages 20−​29), the mean height was 65.8 inches with a standard deviation of 2.87 inches. Answer the following questions about the specified normal distribution.

​(a) The height that represents the 95th percentile is ___.

(b) What height represents the first​ quartile?

22. The weights of bags of baby carrots are normally​ distributed, with a mean of 34 ounces and a standard deviation of 0.31 ounce. Bags in the upper​ 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be​ repackaged?

A bag of baby carrots can weigh at most ___ ounces without needing to be repackaged.

23. A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 35,000 miles and a standard deviation of 2800 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Tires that wear out by __ miles will be replaced free of charge.

24. A vending machine dispenses coffee into a sixteen​-ounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.07 ounce. You can allow the cup to overfill 3​% of the time. What amount should you set as the mean amount of coffee to be​ dispensed?

___ ounces.

25. In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D.

The lowest score that would qualify a student for an A is ___.

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

State the decision rule for 0.10 significance level: H₀: ρ ≤ 0; H₁: ρ > 0.

Compute the value of the test statistic.

Determine the coefficient of determination.

Fill in the blank below. (Round your answer to 1 decimal places.)

___% of the variation in shipping time is explained in by shipping distance

Determine the standard error of estimate.

1. A box contains six 25-watt light bulbs, nine 60-watt light bulbs, and five 100-watt light bulbs. What is the probability a randomly selected a 60 watt light bulb? (PLease explain how did you get your answer)(2 pt) Note: You must provide your answer as a fraction NOT decimal)

2. Cell Phone Provider	Probability
   AT&T	0.271
   Sprint	0.236
   T–Mobile	0.111
   Verizon	0.263

   Does the above table represent the probability model? Explain your answer. (2 pt)

3. The data shows the distance that employees of a certain company travel to work. One of these employees is randomly selected. Determine the probability that the employee travels between 10 and 29 miles to work. (2 pts)

   Distance (miles)	Number of employees
   0 – 9	124
   10 – 19	309
   20 – 29	257
   30 – 39	78
   40 – 49	2

4. In Q3, Is the probability the employee travels between 40 and 49 miles to work considered to be unusual? Explain your answer. (2 pt)

5. The probability that a randomly selected murder resulted from a rifle or shotgun is

   P(rifle or shotgun) = 0.059. Interpret this probability. (2 pt)

   Choose one of the correct answers from below.

   A. If 1000 murders were randomly selected, we would expect about 59 of them to have resulted from a rifle or shotgun.
   B. If any person is randomly selected, there is a 59 % chance the person will be murdered with a rifle or shotgun.
   C. If any person is randomly selected, there is a 5.9% chance the person will be murdered with a rifle or shotgun.
   D. If 1000 murders were randomly selected, exactly 59 of them would have resulted from a rifle or shotgun.

Assume that a new theater is opening near campus. The theater owner wants lots of students to come to see movies, but is nervous about what influences their demand. Through masterful research, the theater owner discovers the following is true about demand for his theater tickets:

Own Price Elasticity    =   3.5      
Cross Price Elasticity    =   2.2      
Income Elasticity    =    4.7

If the owner lowers his price by 20%, by how much will quantity demand change? Show all work.

If the competing theater raises his price by 8%, by how much will quantity demand change at this new theater? Show all work.

If students at the Mount get 9% more income, by how much will demand for tickets change? Show all work.

If incomes fall by 5%, by how much does the theater owner need to lower his price to keep the same number of customers as before? (i.e. to keep quantity demand the same as before the drop in income). Show all work.

1. The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

1. Is the estimated regression equation coefficient for television advertising expenditures the same in par a), in part b) and in part c)? Interpret the coefficient in each case
2. Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
3. What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising, $1800 is spent on newspaper advertising, and $350 in radio advertising?

PLEASE SHOW IN EXCEL AND HOW TO DO IT. Thank you!