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.         What was the manager's return for the month? What was her value-added performance for the month?

b.         What was the contribution of asset allocation to relative performance?

c.         What was the contribution of security selection to relative performance?

To meet increased sales, a large grainery is planning to purchase 2 new dump trucks. Each dump truck will cost $45,000. The salvage value for each truck is $5,000. Total miles over the truck’s useful life is 160,000. Using the units-of-production method, how much is the depreciation for each truck in year 1 when the trucks were driven 14,000 miles?

The speeds of car traveling on Interstate Highway I-35 are normally distributed with a mean of 74
miles per hour and a standard deviation of 6 miles per hour.
(a) Find the percentage of the cars traveling on this highway with a speed
i. of more than 85,
ii. between 65 to 72.
(b) If a BMW is at the speed that is faster than 90 percentage of cars, what is the speed of the
BMW?

A map suggests that Atlanta is 730 miles in a direction 5.00° north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21.0° west of north from Atlanta. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

A bus travels between two cities A and B that are 100 miles apart.Two service stations are located at mile 30 and mile 70, as well as in the cities themselves. The bus breaks down on the road. Assuming the place of breakdown is uniformly distributed between the cities, what is the probability that it is no more than 10 miles to the nearest service station? What is the expectation of the distance to the nearest service station?

The annualized cost of acquiring capacity for the new barracuda drives at Seagate is calculated as $25 per unit and the contibution margin for the product is $45 per unit.

a.) what service level(percentile of demand met) should seagate target for in building capacity? how much capacity will it build? the demand forcast for the barracuda drives is uniform between 100 and 200.

b.) how does this service level change, if Seagate outsources manufacturing to china, to arrive at an annualized cost of capacity of $10 per unit? How much capacity will it build?

c.) How does this service level change if the inbound shipment cost per unit from China to US reduces the margin per unit to $35? How much capacity will it build?

d.) Conduct the capacity calculations in all 3 scenarios above when the forcast for the barracuda drives is expected to follow the following distributions.

Let X1, X2, ..., Xn be a random sample of size from a distribution with probability density function

f(x) = λxλ−1 , 0 < x < 1, λ > 0

a) Get the method of moments estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3.

b) Get the maximum likelihood estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3.

An oil company wants to build a pipeline to take oil from an oil well to a refinery. Unfortunately, the well and the refinery are on either side of a straight river which is 10 miles wide, and they are 50 miles apart along the coastline (that is, if you want to go from the well to the refinery you must first cross 10 miles of river and then go 50 miles along the side of the river). The company has hired you to figure out the cheapest way to build the pipeline, and you need to clearly explain your solution so that the less mathematically-sophisticated oil people will understand.

It costs $200 per mile to lay pipe across the river but only $160 per mile to lay the pipe over land. There is also one other potential cost: It costs extra money each time that you have a bend in the pipeline. If you go straight across the river and use an L-shaped bend it costs an extra $150. If you lay the pipe diagonally across the river but hit land before you get to the refinery, you have to use a slanted L-shaped bend (like an obtuse angle). These have to be custom made and they cost $975. If you go directly diagonally across the river to the refinery without touching any land, then you do not have to pay extra for a bend (since there will not be one).

Exercise 1. Find the cheapest path to lay the pipeline by doing the following:

(a) Draw a diagram of the situation. Include any variables that you are going to use in the rest of your answer.

(b) Calculate the cost of building the pipeline for a few different situations: (i) How much would it cost to build the pipeline 10 miles straight across the river, then make a 90 degree bend and go 50 miles along the side of the river? (ii) How much would it cost to go diagonally across the river, without going on land at all? (iii) Suppose P is the point directly across the river from the oil well. How much would it cost to go diagonally across the river to a point 10 miles along the bank from P, then bend the pipeline and go the remaining 40 miles along the side of the river? (iv) How much would it cost to go diagonally across the river to a point 40 miles along the bank from P, then bend the pipeline and go the remaining distance along the side of the river?

(c) Calculate the cheapest way to build the pipeline for the situation given above by finding the minimum cost among ALL possible locations for P. (i) You will need to write a general expression for the cost of building the pipeline1 , and then use calculus to minimize the cost. (ii) Use either the first or second derivative test to prove that your result is a minimum. (d) What is the effect of the extra cost for a bend in the pipeline? If there was no extra cost for the bend, would you have a different answer for what the cheapest path would be?

Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in table #11.3.3, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer ("Waste run up," 2013). Do the data show that there is a difference between some of the suppliers? Test at the 1% level.

Table #11.3.3: Run-ups for Different Plants Making Levi Strauss Clothing