2. A firm’s production function is given by q= L^1/2+ K. The price of labour is fixed at w = 1, and the price of capital is fixed at r = 8.

a. Find the firm’s marginal rate of technical substitution.

b. Suppose both labour and capital can be varied by the firm, and that the firm wishes to produce q units of output. Use the answer to (a) to find the cost-minimising amounts of labour and capital (as functions of q). You may assume, here and for the other parts of this question, that 4≥ q  .

c. Use the answer to (b) to find the firm’s cost function, and from this, its marginal and average cost functions.

d. For which values of q does this firm face economies of scale? Diseconomies of scale?

e. Explain in words the way this firm expands production as output rises.

International Business

1. Identify and discuss 2 sources of secondary and 2 sources of primary market research.

2. Identify and describe one element of ‘the marketing plan’.

3. Identify and describe two of the five Stages of Exporting.

4. Identify and describe two advantages and two disadvantages of working with a Distributor.

5. Identify and describe the 4 categories of Incoterms.

6. Discuss whether the following terms are an unfair trade advantage: anti-dumping and subsidies.

1.Tier 2 suppliers are primary suppliers to manufacturers. True or False?

2. Which of the following statements is TRUE regarding tier 1 suppliers?

A. Tier 1 suppliers are the starting point of a supply chain.

B. Tier 1 suppliers are the primary suppliers to tier 2 suppliers.

C. Tier 1 suppliers are the primary suppliers to retailers.

D. Tier 1 suppliers are the primary suppliers to manufacturers.

3. Company A fails to satisfy some 15% of customers’ orders last month. What is Company A’s in-stock probability?

A. 15%

B. 85%

C. 100%

D. Cannot be determined

4. A wide and short density function has a large ____________ relative to the _________.

A. standard deviation, mean

B. standard deviation, outcome

C. mean, standard deviation

D. mean, outcome

5 Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 300. Store A purchases the product for $10 each unit and sells each for $25. Inventory is salvaged for $5. What is its maximum profit?

A. $5000

B. $7500

C. $8000

D. $12,500

1)What are constellations, how many are there? 2) What and where is the zodiac? 2)Describe latitude, longitude, prime meridian, RA, Dec, Celestial Equator, and NCP? 3) What is meant by zenith? Altitude, meridian? 4)How do we name the stars? 5)Why is Polaris important? Name *3* things that Polaris can tell us if we find it in the sky! 6)What is the altitude of Polaris in San Mateo? 7)What is meant by circumpolar? 8)How many degrees does your fist span APPROXIMATELY? 9) Describe the Ecliptic, What objects would we find there? 11) Describe the daily(24 hrs), (yearly)and long term(26,000 yrs) motions of the stars 12) What causes the Seasons? Why doesn’t distance from the Sun cause seasons? Describe some evidence that distance doesnt! I put a SEASONS worksheet on Canvas to help you out. You do not need to turn this in! Please contact me for solutions if you have trouble with the questions! 13)What are the solstice, equinox? When do they occur? What special things happen on those dates? 14)How does the Sun move in the sky, where does it rise/set various times of year? 15) Describe precession and its cause 16) Which direction do planets Normally move with respect to the stars? 17) What does the word planet mean in ancient Greek? 18)What is the cause of retrograde motion? 19)Be able to draw and determine Moon phases Be able to determine the rise, transit, and set times for each phase. 20)How long does it take the Moon to go through a complete cycle of phases? 21) How long does it take the Moon to orbit the Earth? 22) Which direction do the planets move around the Sun? (CW or CCW?) 23) What is meant by synchronous rotation? 24) Which direction does the Earth rotate? 25) Why are Uranus’s Seasons so extreme? 26) Be able to identify each phase of the Moon and DRAW the orientation of the Earth Sun and Moon for each phase

1. What is the mean of the sample values 2 cm, 2 cm, 3 cm, 5 cm, and 8 cm?

2. What is the median of the sample values listed in Exercise 1?

3. What is the mode of the sample values listed in Exercise 1?

4. If the standard deviation of a data set is 5.0 ft, what is the variance?

5. If a data set has a mean of 10.0 seconds and a standard deviation of 2.0 seconds, what is the z score corresponding to the time of 4.0 seconds?

6. Fill in the blank: The range, standard deviation, and variance are all measures of _____.

7. What is the symbol used to denote the standard deviation of a sample, and what is the symbol used to denote the standard deviation of a population?

8. What is the symbol used to denote the mean of a sample, and what is the symbol used to denote the mean of a population?

9. Fill in the blank: Approximately _____ percent of the values in a sample are greater than or equal to the 25th percentile.

10. True or false: For any data set, the median is always equal to the 50th percentile.

2a. The two space curves

and

r1(t) = <?1 + 5t, 3 − t^2, 2 + t − t^3> and? r2(s)=< ?3s−2s^2,s+s^3 +s^4,s−s^2 +2s^3>?

both pass through the point P(1,3,2). Find the values of t and s at which the curves pass through this point.

2b. Find the tangent vectors to each curve at the point P (1, 3, 2).

2c. Suppose S is a surface which contains the point P (1, 3, 2), and both r1(t) and r2(s) lie in S. We don’t have an equation for S, but we can still find the equation of the tangent plane to surface S at the point P (1, 3, 2). Use your answers to 2b. to do so:

Find the equation of the tangent plane to S at point P. (Hint: the vectors from 2b. lie in the tangent plane.)

3.

3. The above contour map shows the island of Hawai’i. Suppose that the height above sea level of the island is given by a function z = f(x,y) where (0,0) is at the peak of Mauna Loa and x, y, and z are measured in feet.

3a. If (a, b) is at the point P , determine if each of the following is positive, negative or zero (approximately). Briefly explain your answers. (i) fx (a, b) (ii) fy (a, b) (iii) fxy (a, b) (iv) fxx (a, b)

3b. If Mauna Loa is at a height of 13, 678 feet above sea level, write down the equation of the tangent plane at the point (0, 0).

3c. Approximate the equation of the tangent plane at the point P . Be sure to convert kilometers to feet in your computations!

Calculate:

1) Covariance

2) Expected return on a portfolio XY

2) Risk on a portfolio XY

Weight of each asset is 50%.

Average annual return:

asset X: 11.74%

asset Y: 11.14%

Standard deviation:

asset X: 8.9

asset Y: 2.78

a)

Let y be the solution of the equation  y ′ = (y/x)+1+(y^2/x^2) satisfying the condition  y ( 1 ) = 0. Find the value of the function  f ( x ) = (y ( x ))/x

at  x = e^(pi/4) .

b)

Let y be the solution of the equation  y ′ = (y/x) − (y^2/x^2) satisfying the condition  y ( 1 ) = 1. Find the value of the function  f ( x ) = x/(y(x))

at  x = e  .

c)

Let y be the solution of the equation

y ′ + (3x^2*y)/(1+x^3)=e^x/(1+x^3) satisfying the condition  y ( 0 ) = 1.

Find  ln ⁡ ( 2 y ( 1 ) ).

Upper Division of Lower Company acquired an asset with a cost of $580,000 and a four-year life. The cash flows from the asset, considering the effects of inflation, were scheduled as follows:

The cost of the asset is expected to increase at a rate of 20 percent per year, compounded each year. Performance measures are based on beginning-of-year gross book values for the investment base. Ignore taxes. Required: a. What is the ROI for each year of the asset's life, using a historical cost approach? (Enter your answers as a percentage rounded to 1 decimal place (i.e., 32.1).)

b. What is the ROI for each year of the asset's life if both the investment base and depreciation are determined by the current cost of the asset at the start of each year? (Enter your answers as a percentage rounded to 1 decimal place (i.e., 32.1).)