Northwood Company manufactures basketballs. The company has a ball that sells for $30. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $21.00 per ball, of which 70% is direct labor cost.

Last year, the company sold 53,000 of these balls, with the following results:

.

Required:

1-a. Compute last year's CM ratio and the break-even point in balls. (Do not round intermediate calculations.)

1-b. Compute the the degree of operating leverage at last year’s sales level. (Round your answer to 2 decimal places.)

2. Due to an increase in labor rates, the company estimates that next year's variable expenses will increase by $1.50 per ball. If this change takes place and the selling price per ball remains constant at $30.00, what will be next year's CM ratio and the break-even point in balls? (Do not round intermediate calculations.)

3. Refer to the data in (2) above. If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $99,000, as last year? (Do not round intermediate calculations. Round your answer to the nearest whole unit.)

4. Refer again to the data in (2) above. The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year (as computed in requirement 1a), what selling price per ball must it charge next year to cover the increased labor costs? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

5. Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by 20%, but it would cause fixed expenses per year to increase by 82%. If the new plant is built, what would be the company’s new CM ratio and new break-even point in balls? (Do not round intermediate calculations. Round "Unit sales to break even" to the nearest whole unit.)

6. Refer to the data in (5) above.  

a. If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $99,000, as last year? (Do not round intermediate calculations. Round your answer to the nearest whole unit.)

b-1. Assume the new plant is built and that next year the company manufactures and sells 53,000 balls (the same number as sold last year). Prepare a contribution format income statement (Do not round your intermediate calculations.)

b-2. Compute the degree of operating leverage. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Northwood Company manufactures basketballs. The company has a ball that sells for $36. At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $21.60 per ball, of which 60% is direct labor cost.

this code should be in R.

Write function(s) to drop the smallest one exm grade out of several Exm grades. If a student misses an exm, the grade is NA. You must use NA instead of 0 to represent the value for exms missing. (a) Develop a function to convert an array to another array in which all NA grades are replaced with zero. (b) Complete your function to compute the mean of all elements row by row after dropping exactly one lowest grade. You cannot use any loop statement inside or outside your functions for both (a) and (b). You may use the built-in function in R to find the minimum value in an array. You may use ifelse() only once. You may use the built-in function mean() to find the mean. But be careful! For testing purpose, you may use the following exm grades for each student in each row:

            Exm 1          Exm 2         Exm 3          Exm 4

               80                  NA                90                  NA

               60                  80                  100                NA

               90                  80                  100                40

The average grade of each student must be displayed as a row in a matrix. For the exmple above, you need to display a 3 x 1 matrix with three rows of mean values in one column.

You may use functions: is.na() or na.omit().

Voltage sags and swells. The power quality of a transformer

is measured by the quality of the voltage. Two

causes of poor power quality are “sags” and “swells.” A

sag is an unusual dip and a swell is an unusual increase in

the voltage level of a transformer. The power quality of

transformers built in Turkey was investigated in Electrical

Engineering (Vol. 95, 2013). For a sample of 103 transformers

built for heavy industry, the mean number of sags per

week was 353 and the mean number of swells per week

was 184. Assume the standard deviation of the sag distribution

is 30 sags per week and the standard deviation of the

swell distribution is 25 swells per week.

a. For a sag distribution with any shape, what proportion

of transformers will have between 263 and 443 sags per

week? Which rule did you apply and why?

b. For a sag distribution that is mound-shaped and symmetric,

what proportion of transformers will have between

263 and 443 sags per week? Which rule did you

apply and why?

c. For a swell distribution with any shape, what proportion

of transformers will have between 109 and 259 swells

per week? Which rule did you apply and why?

d. For a swell distribution that is mound-shaped and symmetric,

what proportion of transformers will have between

109 and 259 swells per week? Which rule did you

apply and why?

Here is another infectious disease model. Once a person becomes infected, the time X, in days, until the person becomes infectious (can pass on the disease) can be modeled as a Weibull random variable with density function f(x,α,β) = α βα xα−1e−(x/β)α for 0 ≤ x ≤ ∞ and 0 otherwise with α = 3.7 and β = 7.1 α is the shape parameter and β is the scale parameter. Hint: Solve this with the built-in R functions for the Weibull distribution (dweibull(),pweibull(), qweibull()) not f as defined above. Otherwise you may get intermediate values too large to use. For a) and b) the text (and notes) give formulas for the answers. You can calculate from these formulas. Note that these formulas use the gamma function. Γ(α) is the gamma function. In R, there is a built-in function gamma() which calculates this.

a) What is the expected value of X? 6.4074

b) What is the variance of X? 3.719794

c) What is the standard deviation of X? 1.928677

d) What is the probability that X is larger than its expected value? 0.5045822

e) What is the probability that X is > 2? 0.9908345

f) What is the probability that X is > 4? 0.8872 g) What is the probability that X > 4 given that X > 2?

can you please solve that using R code . please

0.8954249 h) Calculate the 70th percentile of X. 459.273

1. Let W1, . . . , Wn be i.i.d. N(µ, σ²). A 100(1 − α)% confidence interval for σ² is

( ([n − 1]*S² ) / (χ²_{1−α/2,n−1} ) , ([n − 1]S²) / ( χ²_α/2,n−1) ,

where χ²_u,k denotes the 100×uth percentile of the χ² distribution with k degrees of freedom, S² = (n − 1)⁻¹ * the sum of (Wi − Wbar )² (from 1 to n) is the sample variance and Wbar = n⁻¹ * the sum of Wi (from i = 1 to n) the sample mean.

(a) Suppose µ = 68, σ = 4, n = 12, and α = 0.05. Estimate the coverage probability of this random confidence interval for σ² using a Monte Carlo simulation with 1e4 replications. That is, estimate the probability that the confidence interval captures σ² . Denote this estimated probability by pbar. Comment on how 1 − α compares to ±1/ √ 1e4. You may use the qchisq function (hint: the χ² distribution is not symmetric) but you may not use the built in rnorm function.

(b) Estimate the coverage probability for the confidence interval when W1, . . . , Wn are i.i.d. Exp(1). Notice that in this case σ² = var(W1) = 1. Estimate the coverage probability pbar for each (n, α) ∈ {10, 50, 100} × {0.05, 0.1}. In each case, compare 1 − α to pbar ± 1/ √ 1e4. Again, you may not use the built in rexp function. Comment on the results.

USING UNITED STATES IBC CHAPTER 7:

1. Roofing inter-layment shall have a minimum width of ____ inches.

A. 12                           B. 18                           C. 34                           D. 36

2. What is the minimum roof covering classification for a roof assembly on a building of Type IA construction?

A. Class A                   B. Class B                   C. Class C                   D. Non-classified

3. Roof assemblies consisting of metal sheets of shingle are considered ____ as roof assemblies.

A. A                            B. B                             C. C                             D. Special purpose

4. Double underlayment application is required beneath asphalt shingles on roofs having a maximum slope of ______.

A. 2:12                        B. 3:12                        C. 4:12                        D. 5:12

5. In areas subject to high winds, underlayment beneath asphalt shingles shall be fastened along the overlap at a maximum spacing of ____ inches.

A. 12                           B. 18                           C. 24                           D. 36

6. Define the following terms as per code:
     a. Built-up roof covering:

     b. Positive roof drainage:

     c. Scupper:

     d. Roof recover

7. List the test(s) that are used to measure the wind resistance of asphalt shingles.

8. Describe a product that meets the material requirements for wood shingles in roof

9. For built-up roofs, what test standard is used for the use of asphalt in roof?

10. Describe the code requirement in an area where there is a history of ice-forming along the eaves.

subject: International business

Should We Allow Global Corporation to Set Up a Factory in our Country?

About the business.  Global Corporation is applying for planning permission to build a factory in your country. The factory is expected to be very profitable. 1000 new jobs should be created for assembly-line work. Many of the goods made could be sold abroad. Some of the supplies for the factory will come from your country.

About your country.  In your country unemployment is high, especially amongst skilled workers. The government cannot afford any new building projects. There are several local competitors producing goods similar to the Global Corporation. Import levels are very high. Land for new building is very limited. New developments would have to be built in beautiful countryside.

Questions

i. List three groups in your country who may benefit from allowing the Global Corporation to build the factory.(1.5)

ii. List three groups in your country who may lose from the building of the factory.(1.5)

iii. Would you advise your government to allow the new factory to be built? Explain your answer by judging between or evaluating all of the evidence.(3)