The Ambrosia Bakery makes cakes for freezing and subsequent sale. The bakery, which operates 6 days a week, 50 weeks a year, can produce cakes at the rate of 100 cakes per day. The bakery sets up the cake-production operation and produces until a predetermined number (Q) have been produced. When not producing cakes, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of cakes is $600. The cost of holding frozen cakes in storage is $10 per cake per year. The annual demand for frozen cakes, which is constant over time, is 6000 cakes. Determine the following:

1. Optimal production run quantity (Q)

2. Total annual inventory costs

3. Optimal number of production runs per year

4. Optimal cycle time (time between run starts)

5. Run length in working days

Detailed interviews were conducted with over 1,000 street vendors in the city of Puebla, Mexico, in order to study the factors influencing vendors’ incomes. Vendors were defined as individuals working in the street and included vendors with carts and stands on wheels and excluded beggars, drug dealers, and prostitutes. The researchers collected data on gender, age, hours worked per day, annual earnings, and education level. These data are saved in STREETVEN file. Consider an interaction model ? = ?0 + ?1?1 + ?2?2 + ?3?1?2 + ? for the vendor’s mean annual earning ?(?). ?ℎ??? ? = ?????? ????????,?1 = ??? ??? ?2 = ℎ???? ?????? ??? ???.

a. Use statistical software R to fit the interaction model and provide the summary of the model. Also write least squares prediction equation. b. What is the estimated slope relating annual earnings (y) to age (x1) when number of hours worked (x2) is 10? Interpret the result. c. What is the estimated slope relating annual earnings (y) to hours worked (x2) when age (x1) is 40? Interpret the result. d. Conduct a hypothesis test to decide whether age (x1) and hours worked (x2) interact. Write your conclusion.

PLEASE PROVIDE THE CODE FOR R STUDIO or screenshot

VenNum   Earnings   Age   Hours
21   2841   29   12
53   1876   21   8
60   2934   62   10
184   1552   18   10
263   3065   40   11
281   3670   50   11
354   2005   65   5
401   3215   44   8
515   1930   17   8
633   2010   70   6
677   3111   20   9
710   2882   29   9
800   1683   15   5
914   1817   14   7
997   4066   33   12

You want to determine whether there is a statistically different average weekly sales between Sales Rep A and Sales Rep B.

* Create Null and Alternative Hypothesis statements that would allow you to determine whether their sales performance is statistically different or not.

* Use a significance level of .05 to conduct a t-test of independent samples to compare the average weekly sales of the two candidates.

* Calculate the p-value?

1. Jon, Sara, Rohit, and Maria currently earn $100k, $120k, $40, and $20. Assume utility function is U(y)=(y)^(0.5).   Consider a utilitarian social planner deciding on whether to enact the following policy: tax 10% for all earnings above $50k, and transfer it as a lump sum to all earning below $50. Assume further that 30% of the potential revenue based on current earnings is “lost” (leaky bucket) due to reduced work incentives.

Q1. In a class of 50 students, the number of students who offer Accounting is twice as the number who offer Economics. 10 students offer neither of the two students and 5 student offer both subjects.
i.) Illustrate the information on a Venn diagram.
ii.) How many students offer Accounting?
iii.) How many students offer only one subjects?

Q2. In a class of 60 students, the number of students who passed Biology is 6 more than the number who passed chemistry. Every student passed at least one of the two subjects and 8 students passed both subjects.
i.) How many students passed Biology?
ii.) How many students passed Chemistry?
iii.) How many students passed only one subjects?

Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers/two-night package; convention customers/Friday night only; convention customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only; and regular customers/Saturday night only.

The cost for each type of reservation is shown here:

The anticipated demand for each type of reservation is as follows:

Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.

1. Define the decision variables and state the objective function. Round your answers to the nearest whole number.
   

   Let	CT = number of convention two-night rooms
   	CF = number of convention Friday only rooms
   	CS = number of convention Saturday only rooms
   	RT = number of regular two-night rooms
   	RF = number of regular Friday only rooms
   	RS = number of regular Saturday only room

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

2. Formulate a linear programming model for this revenue management application. Round your answers to the nearest whole number. If the constant is "1" it must be entered in the box.
   

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

   S.T.

   1)	CT
   2)	CF
   3)	CS
   4)	RT
   5)	RF
   6)	RS
   7)	CT	+	CF
   8)	CT	+	CS
   9)	CT	+	CF	+	RT	+	RF
   10)	CT	+	CS	+	RT	+	RS
   11)	CT,	CF,	CS,	RT,	RF,	RS			0

3. What are the optimal allocation and the anticipated total revenue? Round your answers to the nearest whole number.
   

   Variable	Value
   CT
   CF
   CS
   RT
   RF
   RS

   
   Total Revenue = $  
   
4. Suppose that one week before the convention the number of regular customers/Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accepting this additional reservation? Round your answer to the nearest dollar.
   
   The dual value for constraint 10 shows an added profit of $   if this additional reservation is accepted.

Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers/two-night package; convention customers/Friday night only; convention customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only; and regular customers/Saturday night only.

The cost for each type of reservation is shown here:

The anticipated demand for each type of reservation is as follows:

Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.

1. Define the decision variables and state the objective function. Round your answers to the nearest whole number.
   

   Let	CT = number of convention two-night rooms
   	CF = number of convention Friday only rooms
   	CS = number of convention Saturday only rooms
   	RT = number of regular two-night rooms
   	RF = number of regular Friday only rooms
   	RS = number of regular Saturday only room

   Max

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

2. Formulate a linear programming model for this revenue management application. Round your answers to the nearest whole number. If the constant is "1" it must be entered in the box.
   

   Max

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

   S.T.

   1)	CT	<
   2)	CF	<
   3)	CS	<
   4)	RT	<
   5)	RF	<
   6)	RS	<
   7)	CT	+	CF	≥
   8)	CT	+	CS	≥
   9)	CT	+	CF	+	RT	+	RF	≤
   10)	CT	+	CS	+	RT	+	RS	≤
   11)	CT,	CF,	CS,	RT,	RF,	RS		≥	0

3. What are the optimal allocation and the anticipated total revenue? Round your answers to the nearest whole number.
   

   Variable	Value
   CT
   CF
   CS
   RT
   RF
   RS

   
   Total Revenue = $  
   
4. Suppose that one week before the convention the number of regular customers/Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accepting this additional reservation? Round your answer to the nearest dollar.
   
   The dual value for constraint 10 shows an added profit of $   if this additional reservation is accepted.

New Balance, a major athletic-wear company, is dissatisfied with the number of employee days lost due to sickness. Per employee, the mean number of days lost per year is 21, and the standard deviation is 5. In order to try to reduce this loss, the board of directors appoint an occupational psychologist to make recommendations for changes in corporate policy. The psychologist suggests that providing free fitness classes at lunchtimes could help. The directors agree to try providing these classes at one corporate location. After one year, the number of days lost for each employee at the corporate location is as follows: 25, 26, 16, 15, 26, 14, 23, 4, 17, 21, 22, 5, 14, 20, 10, 18 a) Represent the null and alternative hypotheses in symbol form b) Identify the rejection region using  = 0.05 for a two-tailed test. Draw a rough graph showing the critical region. c) What conclusions can be drawn from this study about the effect of providing free fitness classes on the number of employee days lost due to sickness? Be sure to state your conclusions in plain English.

The distribution of Master’s degrees conferred by a university is listed in the table.

What is the probability that a randomly selected student graduating with a Master’s degree has a major of Education or a major of Engineering?

A. 0.371 B. 0.720 C. 0.390 D. 0.280

2.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam.

A). Calculate the correlation coefficient.

B). Find the equation of the regression line.

C). Use the regression equation to predict the test score of a student who studied for 5.5 hours.

3. Find the ?-score for which 70% of the distribution’s area lies to its right.

A. -0.52 B. -0.98 C. -0.48 D. -0.81

4. A group of 49 randomly selected students has a mean age of 22.4 years. Assume the population standard deviation is 3.8. Construct a 98% confidence interval for the population mean.

A. (20.3, 24.5) B. (18.8, 26.3) C. (21.1, 23.7) D. (19.8, 25.1)

5.Use fundamental counting principle to determine how many license plates can be made consisting of 3 different letters followed by 2 different digits.

A. 1,757,600 B. 175,760 C. 100,000 D. 1,404,000

6. A group of students were asked if they carry a credit card. The responses are listed in the table.

If a student is selected at random, find the probability that he/she owns a credit card given that the student is a freshman.

A. 0.400 B. 0.615 C. 0.667 D. 0.333

7. Use the standard normal distribution to find ?(−2.50 < ? < 1.50).

A. 0.8822 B. 0.5496 C. 0.6167 D. 0.9270

8.

The number of home runs that Barry Bond hit in the first 18 years of his major league career are listed.

16 25 24 19 33 25 37 41 37

25 42 40 37 34 49 73 46 45

A). Find the mean.

B). Find the median.

C). Find the mode.

At t = 0s, the leading edge of a wave (wavelength 1m) is 3m to the left of a boundary. The wave is moving to the right at 1m/s. The transmitted wave has wavelength 3m. (You may draw pictures to help you answer the questions below, but you must explicitly state - in words - the answers to the questions.)

(a)[8 pt(s) ]At t = 5s, where is the leading edge of the transmitted wave? Is the transmitted wave inverted or non-inverted, and why?