A potential buyer of a sportscar is interested in the costs of a vehicle per mile travelled at net present value. The buyer is planning to sell the car after three years of operation at residual value.

The car costs £35000.00 to purchase and the buyer incurs costs for insurance, fuel and mantenance of £1400.00 per year. The car is expected to depreciate in value by £4000.00 per year (straight line depreciation). The buyer is planning to travel 17000 miles per year.

What is the total cost of ownership per mile travelled at net present value, assuming that all payments arise annually and are subject to an annual discount rate of 3%. Note that the miles travelled are not subject to discounting.

Suppose the given country road has large defects which are distributed along its length according to Poisson distribution with an average of 2 defects per mile. It takes the crew repairing these defects one full day to fix one of them. They move along the road and repair the defects as they are found.

a) If the road is 10 miles long what is the probability they will be done in three weeks (15 working days)?

b) What is the probability they will get at least to the middle of the road (i.e. advance by at least 5 miles) by the end of the second week (after 10 working days)?

c) What is the mean and standard deviation of the length of the road they will cover by the end of the second week?

For the following situations, develop the appropriate Ho and Ha and state what the consequences would be for Type 1 and Type 2 errors.

a. A company that manufactures one-half inch bolts selects a random sample of bolts to determine if the diameter of the bolts differs significantly from the required one-half inch.

b. A company that manufactures safety flares randomly selects 100 flares to determine if the flares last at least three hours on average.

c. a consumer group believes that a new sports coupe gets significantly fewer miles to the gallon than advertised on the sales sticker. To confirm this belief, they randomly select several of the new coupes and measure the miles per gallon.

Suppose the given country road has large defects which are distributed along its length according to Poisson distribution with an average of 2 defects per mile. It takes the crew repairing these defects one full day to fix one of them. They move along the road and repair the defects as they are found. a) If the road is 10 miles long what is the probability they will be done in three weeks (15 working days)? b) What is the probability they will get at least to the middle of the road (i.e. advance by at least 5 miles) by the end of the second week (after 10 working days)? c) What is the mean and standard deviation of the length of the road they will cover by the end of the second week?

A. Calculate the price of pit-run gravel delivered to the site per cubic yard (bank measure) based on the following data: The pit is located 10 miles from the site. Trucks cost $43.75 per hour including fuel and maintenance; they have 12 cubic yards (loose material) capacity and travel at an average speed of 30 miles per hour. The swell factor for this material is 15%. Trucks take 5 minutes to unload at the site. The loader costs $82.50 per hour and loads material at the pit at the rate of 40 cubic yards per hour. The truck driver’s wage is $45.00 per hour, and the equipment operator’s wage is $54.00 per hour.

I need to know how to answer this question only in Excel. Please include instructions, screenshots, etc. in Excel which explain the process (formulas included).

TropSun is a leading grower and distributer of fresh citrus products with three large citrus groves scattered around central Florida in the cities of Orlando, Eustis, and Winter Haven. TropSun currently has 275,000 bushels of citrus at the grove in Mt. Dora, 400,000 bushels at the groves in Eustis, and 300,000 bushels at the grove in Clermont. TropSun has citrus processing plants in Ocala, Orlando, and Leesburg with processing capabilities to handle 200,000, 600,000, and 225,000 bushels respectively. TropSun contracts with a local trucking company to transport its fruit from the groves to the processing plant. The trucking company charges a flat rate for each mile that each bushel of fruit must be transported. Each mile a bushel of fruit travels is known as a bushel-mile. The following table summarizes the distances (in miles) between the groves and processing plant.

TropSun wants to determine how many bushels to ship from each grove to each processing plant to minimize the total number of bushel-miles the fruit must be ship. [ Another way to put it, MINIMIZE the TRANSPORTATION costs of the bushel-miles from the groves to the Plants] (30 Points) HINT: What decision variables can change.

1. Define the decision variables.

2. Define the Constraints

3. Implement and Solve the Problem in Excel

4. Analyze the Solution, what is it telling the decision maker?

Wayne Collier designed an experiment to measure the
fuel efficiency of his family car under different tire pressures.
For each run, he set the tire pressure and then measured the
miles he drove on a highway (I-95 between Mills River and
Pisgah Forest, NC) until he ran out of fuel using 2 liters of fuel
each time. To do this, he made some alterations to the normal
flow of gasoline to the engine. In Wayne’s words, “I inserted
a T-junction into the fuel line just before the fuel filter, and a
line into the passenger compartment of my car, where it joined
with a graduated 2 liter Rubbermaid© bottle that I mounted in
d©
a box where the passenger seat is normally fastened. Then I
sealed off the fuel-return line, which under normal operation
sends excess fuel from the fuel pump back to the fuel tank.”
Suppose that you call the mean miles that he can drive with
µ.
µ
normal pressure in the tires
An unbiased estimate for
is the
mean of the sample runs, x. But Wayne has a different idea. He
decides to use the following estimator: He flips a fair coin. If the
coin comes up heads, he will add five miles to each observation.
If tails come up, he will subtract five miles from each observation.
(a) Show that Wayne’s estimate is, in fact, unbiased.
(b) Compare the standard deviation of Wayne’s estimate with
the standard deviation of the sample mean.
(c) Given your answer to (b), why does Wayne’s estimate not
make good sense scientifically

It is a calm summer day in southeast Iowa at the Ottumwa air traffic control radar installation - except there are some small, locally intense thunderstorms passing through the general area. Only two planes are in the vicinity of the station: American Flight 1003 is traveling from Minneapolis to New Orleans is approaching from the north-northwest, and United Flight 336 is traveling from Los Angeles to New York is approaching from west-southwest. Both are on the path that will take them directly over the radar tower. There is plenty of time for the controllers to adjust the flight paths to insure a safe separation of the aircraft.

Suddenly lightning strikes a power substation five miles away, knocking out the power to the ATC installation. There is, of course, a gasoline powered auxiliary generator, but it fails to start. In desperation, a mechanic rushes outside and kicks the generator; it sputters to life. As the radar screen flickers on, the controllers find that both flights are at 33,000 feet. The American flight is 32 nautical miles (horizontally) from the tower and is approaching it on a heading of 171 degrees at a rate of 405 knots. The United flight is 44 nautical miles from the tower and is approaching it on a heading of 81 degrees at a rate of 465 knots.

a. At the instant of this observation, how fast is the distance between the planes decreasing?
b. How close will the planes come to each other?
c. Will they violate the FAA's minimum separation requirement of 5 nautical miles?
d. How many minutes do the controllers have before the time of closest approach?
e. Should the controllers run away from the tower as fast as possible?

The specific questions asked above are a guide to your work and suggestions of the directions to pursue. Your report must contain not just answers to questions but explanations as well.

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month. (Round your answers to 1 decimal place.)

1-b. Compute the manufacturing cycle efficiency (MCE) for each month. (Round your answers to 1 decimal place.)

1-c. Compute the delivery cycle time for each month. (Round your answers to 1 decimal place.)

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

If x is a binomial random variable, compute P(x) for each of the following cases:

(a) P(x≤5),n=7,p=0.3

P(x)=

(b) P(x>6),n=9,p=0.2

P(x)=

(c) P(x<6),n=8,p=0.1

P(x)=

(d) P(x≥5),n=9,p=0.3

P(x)=