A firm has a production function Q = KL, where Q is the quantity of output, K is the amount of capital and L is the amount of labor. MPL=K and MPK=L .

a) Suppose that capital is fixed at K=10 in short run. In this case, the marginal product of labor is MPL=10. Does this production function exhibit diminishing marginal returns to labor?

b) Suppose that in the short run, K is fixed at 10. The interest rate is r=4 and the wage is w=1. What is the short run total cost curve?

c) In (b), what are the functions for fixed cost, variable cost, average fixed cost, average variable cost and average cost?

d) In the long-run, capital is also variable. Does this production function exhibit increasing, decreasing or constant returns to scale?

(A-D HAS BEEN ANSWERED)

e) What is the long run cost function? What is average cost in the long run?

A.The long run total cost function is C = 4Q^1/2 and the average cost is AC = 4Q^–1/2.

B.The long run total cost is C = L + 4K and the average cost is AC = (L+4K)/Q

C.The long run total cost function is C = 4L + K and the average cost is AC = 4 + K

D.The long run total cost function is C = 4√Q and the average cost is AC = 4/Q.

f) Does this cost function exhibit increasing or decreasing economies of scale?

A. This cost function exhibits economies of scale

B. This cost function exhibits diseconomies of scale

C. This cost function exhibits neither economies nor diseconomies of scale

D. This production function exhibits economies of scale

Flexural strength design check of sections of a typical internal portal frame:

The load cases which you are expected to analyse for portal frame in this exercise, and from which the design bending moments and the coincident axial forces required for this section should be derived, are discussed in the ‘Supplementary Notes’. The moment capacities Msx and Mbx and the axial capacities Ns, Ncx and Ncy may be determined using the tables in the AISC ‘Design Capacity Tables for Structural Steel’ publication.

Rafters:
Check the flexural strength of the rafters in a typical internal portal frame, in the general vicinity of the ridge. Again, check for the two cases of maximum sagging B.M. at or near the ridge and maximum hogging B.M. at or near the ridge, and allow for the coincident axial force. Again, note that:
 The purlins in the roof are at 1250mm centres, generally.
 Assume there is fly bracing at the ridge and then at 4 spaces from the ridge (obtain value depending on frame geometry).
For the rafters assume Grade 300 steel.

Retrograde motion of superior planet always occurs when the planet is a) in conjunction with the moon b)brighter than average c)near the autumnal equinox d) near a solstice e) dimmer than average 2) The moon a) spins once on its axis relative to the sun every 23 hours 56 mins. b) spins once on it axis relative to the sun every 24 hours c) spins once on its axis relative to the sun every 29.5 days d) spins once on its axis relative to the sun every 365 days e)never spins on its axis 3) The planets a) move faster in their orbit around the sun in km/s, the closer they are to the sun b) are always located at the same right ascension and declination in the sky c) are always found along the celestial equator d) are always located at declinations greater than 60 degrees e) are always observed along the meridian

A study was conducted to investigate the hypothesis that living within 100 meters of a large highway increased the risk of childhood respiratory illness. The investigators recruited 200 children ages 6 to 10 years old living near highways and another 200 children of similar age, gender and ethnicity living more than 100 meters from highways. They followed the children for 3 months and asked the parents to record in a daily diary any symptoms of respiratory illness. At the end of the 3 months, 36 of the 200 “exposed” children (living near a highway) had developed at least one respiratory illness, while 17 of the 200 living further away had developed respiratory illness. a. What kind of study was this? b. What measure of disease frequency can be calculated? Calculate it for each group and interpret the results. c. What measure of association can be calculated? Calculate it and interpret the results.

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

(a) Construct a boxplot of the data.

Comment on any interesting features. (Select all that apply.)

The data appears to be centered near 428.There are no outliers.The data appears to be centered near 438.There is one outlier.There is little or no skew.The data is strongly skewed.

(b) Is it plausible that the given sample observations were selected from a normal distribution?

YesNo    

(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.)

  ,

Does the interval suggest that 443 is a plausible value for true average degree of polymerization?

YesNo    

Does the interval suggest that 450 is a plausible value?

YesNo    

3. Analyze and Journalize the following entries; On June 1, 2012 Sam Near created a travel agency called Tours-For-Less. These activities occurred during the company’s first month:

(Q=610-110-3.AcctsRec3_week4)

INVENTORY CARDS

Sets Of Sting Ray Golf Clubs

(Q=630.Inventory3_week4)

Pairs Of Football Boots

(Q=630.Inventory4_week4)

Quidditch Snitches

(Q=630.Inventory5_week4)

Specialist Tennis Raquets

Answer the following questions: a. Suppose that a firm is producing where 0 < MR < MC. What would happen to total revenue, total cost, and profit if the firm produced one less unit of output? b. Suppose that a firm is producing where MR > MC. What would happen to total revenue, total cost, and profit if the firm produced one more unit of output? c. If a firm produces the next unit of output, total revenue rises from $12,000 to $13,500 and the marginal cost of the next unit is $1,700. Should the firm produce the next unit of output? Question 34 options:

Hello and Happy Holidays...Can you get me started on this question? Thanks in advance!

If two large companies merge, why might you want to run a multi-objective optimization to trade off the total cost of company one versus the total cost to company two? That is, why might this be better than running with just the objective of minimizing the total cost of the combined supply chain?

Part A

Charles loves Mello Yello and will spend $8 per week on the product no matter what the price.

True or False: Charles’s demand for Mello Yello is unitary elastic.

Part B

Suppose there is a decrease in the demand for high-definition televisions.

The short-run average total cost curve for this product will ________ (Increase/Decrease/Not Change) because:

a. When demand decreases, the short-run average total cost increases.

b. Short-run average total cost depends on workers’ wage rates and the prices of inputs rather than on demand.

c. When demand decreases, the short-run average total cost declines.