Suppose a firm's marginal product of capital and marginal product of labor schedules are as shown in the table below. The firm hires both capital and labor competitively for $5 and $8, respectively. This assignment will be graded out of 6 points with 2 points possible for each question.

1. Suppose the firm is currently using 4 units of capital and 4 units of labor. Is the corresponding output being produced at least cost? How do you know?

2. Consider your answer to the question above. Generally speaking, what would a firm need to do in order to move towards producing at the least cost?

3. What is the least-cost combination of labor and capital?

Create an ERD chart that prevents data redundancies and anomalies. The entire primary key must determine the values in the other columns of a table. No non-key column should determine the value of another column.

The data this system must store:

Property lot numbers and their corresponding addresses

Owners’ last names and first names

Owners’ various phone numbers

Owners various email addresses

Owner various mailing addresses and the months when they reside at them

The relationship between owners and properties

On January 1, 2018, Corp X issued 3%, 3 ½ year Bonds to the public, and also signed a 3 and 1/2 -year lease with PH Corp. Payments of $10,000 on the lease are made at the end of the year for years 1,2 and 3 and ($5,000 in the last period; year 4.) There are no provisions for a bargain purchase or an extension of the lease term. The asset has a fair value of $35,000 and has a useful economic life of 4 years.

Corp. X is rated as a BBB rated company by Moody’s Investors-a rating company.

Additional Facts

1-BBB Market Interest rates:

Date of issue                         on 12/31/2019

Year 1     2%                               1.5%

Year 2    2.5%                            2.0%

Year 3    2.75%                          2.5%

Year 4    3,5%                             3.0%

Year 5     4.0%.                           4.0%

BTW There is no correct answer

Question 7

1-Calculate the market interest rate at date of issue?

2-Calculate the price of the bond at the date of issue?

3-What is the interest expense in Year 1.

4-What is the Balance Sheet value of Bonds payable on 12/31/19? Please provide 2 answers.

On January 1, 2018, Corp X issued 3%, 3 ½ year Bonds to the public, and also signed a 3 and 1/2 -year lease with PH Corp. Payments of $10,000 on the lease are made at the end of the year for years 1,2 and 3 and ($5,000 in the last period; year 4.) There are no provisions for a bargain purchase or an extension of the lease term. The asset has a fair value of $35,000 and has a useful economic life of 4 years.

Corp. X is rated as a BBB rated company by Moody’s Investors-a rating company.

Additional Facts

1-BBB Market Interest rates:

Date of issue                         on 12/31/2019

Year 1     2%                               1.5%

Year 2    2.5%                            2.0%

Year 3    2.75%                          2.5%

Year 4    3,5%                             3.0%

Year 5     4.0%.                           4.0%

BTW There is no correct answer

Question 7

1-Calculate the market interest rate at date of issue?

2-Calculate the price of the bond at the date of issue?

3-What is the interest expense in Year 1.

4-What is the Balance Sheet value of Bonds payable on 12/31/19? Please provide 2 answers.

Ch.8 #5

Consider the following time series data.

1)  Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

Value = ________ + __________ Qtr1 + ___________ Qtr2 + ___________ Qtr3

2) Compute the quarterly forecasts for next year based on the model you developed in part (b). If required, round your answers to three decimal places. Do not round intermediate calculation.

Quarter 1 forecast _____________

Quarter 2 forecast_____________

Quarter 3 forecast_____________

Quarter 4 forecast_____________

3) Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

Value = __________ + __________ Qtr1 + __________ Qtr2 + ___________ Qtr3 + ________ t

4) Compute the quarterly forecasts for next year based on the model you developed in part (d).

Quarter 1 forecast _____________

Quarter 2 forecast_____________

Quarter 3 forecast_____________

Quarter 4 forecast_____________

5) Is the model you developed in part (b) or the model you developed in part (d) more effective?

Justify your answer.

A bridge hand is found by takinf 13 cards at random and without replacement from a deck of 52 playing cards. Find the probability of drawing each of the following hands.

(a) One in which there are 5 spades, 4 hearts, 3 diamonds and 1club.

(b) One in which there are 5 spades, 4 hearts, 2 diamonds and 1 club.

(c) One in which there are 5 spades, 4 hearts, 2 diamond, and 3 clubs.

(d) Suppose you are dealt 5 cards of one suit, 4 cards of another. Would the probability of having the other suits split 3 and 1 be greater than the probability of having them split 2 and 2?

1. Sort the given keys using Counting sort algorithm. Also write the algorithm.

         4, 1, 0, 2, 1, 5, 0, 4                                                                    

No code or programs, please. Manually solve the problem, please. Thanks

Question 2. The quarterly sales of the TRK-50 mountain bike for the previous four years by a bicycle shop in Switzerland are presented in the table:

1. Plot the sales against time.
2. Use the data to estimate the monthly trend in sales using a linear trend model of the form:
   Q_t = a + bt. Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend at 5 percent level of significance?
3. Now adjust your statistical model to account for seasonal variation in sales. Estimate this model of sales:
   Q_t = a + bt + cD₂ + dD₃ + eD₄
   where D₂, D₃, D₄ are the appropriately defined dummy variables for quarters 2, 3, and 4.
   Do the data indicate a statistically significant seasonal pattern at 5 percent level of significance? If so, what is the seasonal pattern of sales?
4. Comparing your estimates of the trend in sales in parts b and c, which estimate is likely to be more accurate? Why?
5. Using the estimated forecast equation from part c, forecast sales for Quarters 1 and 4 of 2014 and Quarters 2 and 3 of 2015.

find the point lying on the intersection of the plane, x + (1/4)y + (1/3)z = 0 and the sphere x 2 + y 2 + z 2 = 25 with the largest z-coordinate. (x,y,z)=(_)

Solve a system of equations:
1-
2x = 5 mod 15  
3x = 1 mod 4

2-
x = 5 mod 15
x = 2 mod 12

(Hint: Note that 15 and 12 are not relatively prime. Use the Chinese remainder
theorem to split the last equation into equations modulo 4 and modulo 3)