Probability and Decision Analysis

A smartphone supplier in Sydney is considering three alternative investment options: a large store, a small store, or an outlet in the shopping mall.  

Profits from selling smartphones will be affected by the customer demand for smartphones in Sydney. The following payoff table shows the profit that could result from each investment, in dollars ($).  

1. What choice should be made by the optimistic decision maker?

2. What choice should be made by the pessimistic decision maker?

3. Compute the regrettable from the data.

4. What decision should be made under minimax regret approach?

5. What choice should be made under the expected value approach?

With excel

In order to improve the financial Situation of Thoughts, the Manager looked into expansion plans and decided to offer caterings for events. For the catering business, the manager is offering his customers a selling price p that depends on demand, where p= 9 - 0.02*D.

a- Calculate the Quantity that Maximises Revenue.

b- Calculate the Quantity that Maximises Profit (Refer to problem 1 for costs).

Problem 1 Costs:

Rental $80 per day

Coffee beans $5 per Coffee Cup

Sugar $0.3 per Coffee Cup

Flavors $ 0.5 per Coffee Cup

Filtered water $0.2 per Coffee Cup

Labor $30 per day

c- Calculate the Breakeven point(s).

No Ready-to use Formula should be used in this Problem, show your iterations. Ready-to-use formulas and Calculator-derived results will NOT be accepted

A factory wants to improve its service capacity by purchasing a new machine. Three different machines are available. The table below displays the estimated profits for all combinations of decisions with outcomes.

Questions:

1. In case of uncertainty, apply the Maximax and Maximin criteria to find the corresponding best decision.
2. Use the expected monetary value (EMV) method to find the best decision.
3. A data analytic company proposed to the decision maker certain information about the market condition for $3000. Should the decision maker purchase the information for that price? Explain why.

and please the answer is typed

An amusement park has estimated the following demand equation for the average park guest

Q=16?2P

Where Q represents the number of rides per guest and P the price per ride. The total cost of providing rides to a guest is

TC=2+0.5Q

If a one-price policy is used, how much should it charge per ride if the park wishes to maximize its profit?

What is the park's profit for each guest?

If a two-part tariff policy is used, what admission fee should the park charge to maximize its profit?

What is the park's profit for each guest?

A survey of 1320 people who took trips revealed that 108 of them included a visit to a theme park. Based on those survey results, a management consultant claims that less than 9 % of trips include a theme park visit. Test this claim using the ?=0.05

significance level.

Find

(a) The test statistic

(b) The P-value

(c) A or B in conclusion
A. There is not sufficient evidence to support the claim that less than 9 % of trips include a theme park visit.
B. There is sufficient evidence to support the claim that less than 9 % of trips include a theme park visit.

Consider the following hypothetical scenario: The city council has just approved the construction of an amusement park in your town. You are responsible for studying the impact of the new amusement park on the local economy and the surrounding community. Write a paper of approximately 500 words that addresses all of the questions below. Include the graphs, where indicated: o Question 1: You know that the amusement park will increase the traffic flow in the streets around the amusement park. There are both businesses and neighborhoods adjacent to the increased traffic flow. The cost to the community is estimated to be $6 per person.  What kind of externality is this? Why? o Graph the market for amusement park business, labeling the demand curve, the social-value curve, the market equilibrium level of output, and the socially optimal level of output.  What is the per-unit amount of the externality? o Question 2. You know that the amusement park will have events in the evening. This will increase both foot traffic and street traffic at night. You believe this will improve the safety of the surrounding businesses, with an estimated benefit of $2 per park attendee. What kind of externality is this? Why? o Question 3 Create a new graph illustrating the market for amusement park business for these two externalities together. Label the demand curve, the social-value curve, the market equilibrium level of output, and the final socially optimal level of output.  What is the per-unit amount when both externalities are considered?  Discuss both government and private solutions that would result in an socially optimal outcome.

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month. (Round your answers to 1 decimal place.)

1-b. Compute the manufacturing cycle efficiency (MCE) for each month. (Round your answers to 1 decimal place.)

1-c. Compute the delivery cycle time for each month. (Round your answers to 1 decimal place.)

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE. (Round your answers to 1 decimal place.)

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b)Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0  

   H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We cannot conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.    

Do not reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We conclude that the relationship is significant.

(c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = β₀ + β₁x + ε where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b₀ + b₁x + b₂x²

(a) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x².  (Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b) Use α = 0.01 to test for a significant relationship. State the null and alternative hypotheses.

H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0   

  H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0

H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.   

Do not reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We cannot conclude that the relationship is significant.

(c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

• y = traffic flow in vehicles per hour
• x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b)

Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0 H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0      H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero. H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We cannot conclude that the relationship is significant.

Do not reject H₀. We conclude that the relationship is significant.    

Reject H₀. We cannot conclude that the relationship is significant.

Reject H₀. We conclude that the relationship is significant.

(c)

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour