Study the variation in the optimal solution of the following parameterized LP, given t≥ 0: Minimize z = 4x1 + x₂ + 2x3
Answers
Given LP, Minimize z = 4x1 + x2 + 2x3for t ≥ 0.Observe that the given LP has no constraints or any bounds for the variables x1, x2 and x3. The minimum value of z is given by, Minimum value of z = z* = 2t + 5/4, for t ≥ 5.In summary, the minimum value of z is,-∞ for t = 0,2t for 0 < t ≤ 2,2t + 5/4 for t ≥ 5.
Now, let's look at the various cases for t.
1) For t = 0:For t = 0, the given LP is, Minimize z = 4x1 + x2 + 2x3. Here, the objective function is unbounded below because we can make z as small as we want by taking the variables x1 and x3 to be negative and x2 to be large and negative. Hence, the minimum value of z is -∞.
2) For t > 0:For t > 0, the given LP is, Minimize z = 4x1 + x2 + 2x3Subject to,x1 + x2 + x3 ≥ t (Call this constraint C1)
Now, let's consider two cases:
Case 1: t ≤ 2If t ≤ 2, then we can take x1 = x2 = x3 = t/3 to satisfy constraint C1.
Case 2: t > 2If t > 2, then constraint C1 is binding. Let x1, x2 and x3 be the optimal values that satisfy constraint C1.
Now, let's consider two cases:
Case 2.1: 2 < t < 5For 2 < t < 5, we can see that the dual problem is infeasible.
Case 2.2: t ≥ 5For t ≥ 5, we can see that the dual problem is feasible and has a finite optimal solution. T
Therefore, the dual problem is feasible and has a finite optimal solution. Hence, by strong duality, the primal problem also has a finite optimal solution. Let's call the optimal value of the primal problem z*.Then, by strong duality, we have z* = 2t + 5/4.
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Related Questions
What are the advantages of a private limited company rather than a partnership as a form of business organisation?
Answers
Answer:
Owners of a partnership are liable for business debts and obligations. Private limited companies are owned by shareholders and managed by directors. They carry limited liability for business debts, which reduces personal risk.
Why is it important to demonstrate a positive work attitude in the workplace?
O to be seen as trustworthy and reliable
O to be seen as coachable and flexible
O to be seen as willing to delegate tasks
O to be seen as easily persuadable
Answers
Answer:
the first one
Explanation:
if you aren't trustworthy you might not get as many opportunities in your workplace
true or false? a contractor facility may store classified material as soon as the facility clearance (fcl) is granted.
Answers
The given statement "a contractor facility may store classified material as soon as the facility clearance (fcl) is granted" is false.
A contractor facility cannot store classified material as soon as the facility clearance (FCL) is granted. While obtaining an FCL allows the contractor facility to access and handle classified information, there are additional security measures and procedures that need to be in place before storing classified material.
Once the facility clearance is granted, the contractor facility must establish and implement specific security measures to ensure the proper handling, storage, and protection of classified material.
These security measures may include physical security controls, personnel security requirements, information systems security, and adherence to specific security protocols outlined by the government agency responsible for the classified material.
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A grocery store orders their monthly food order from a distributor. The food is scheduled to be delivered by the next Friday. Which pathways in the Transportation and Logistic career cluster are involved in this entire process? Facility and Mobile Equipment Maintenance, Sales and Service; Transportation Operations; and Health, Safety and Environmental Management Transportation Systems/Infrastructure Planning, Management, and Regulation, and Facility and Mobile Equipment Maintenance Transportation Operations, Warehousing and Distribution Center Operations; Logistics Planning and Management Services; and Sales and Service Health, Safety and Environmental Management and Transportation Systems/Infrastructure Planning, Management, and Regulation
Answers
Answer:
For the food to be delivered successfully by the grocery store, the following pathways needs to be followed to achieve that:
Facility and Mobile Equipment Maintenance,
Sales and Service;
Transportation Operations; and Health,
Safety and Environmental Management Transportation.
Explanation:
This process is true because, there is need to ensure that, the facility and mobile equipment is well maintained to avoid breakdown of the equipment during transportation.
The last pathway to ensure successful delivery happens to be safety and environment management transportation since what is being dealt with happens to be food that is going to be eaten. Maximum care is taken to ensure there is no contamination whatsoever.
Answer:
Option A is correct
Explanation:
Just took the test :)
Happy New Year everyone, here's to 2021
How can you say that Economics is a science of choice??
Answers
Answer:
Your answer is attached above
hope it helps
and I want to talk to you kavya sis
It's really important plzz dont ignore plzzz
If you want to become a firefighter what are some steps you need to take to get there?
Answers
Answer:
All the best :)Explanation:
1: Make Sure You're Fit to be a Firefighter.
2: Meet the Requirements & Take the Tests.
3: Prepare for a Firefighting Career: Education Options.
4: Become Trained as an EMT.
5: Receive Firefighter Training at a Fire Academy.
6: Apply to Your Firefighting Dream Jobs.
The upscale hotel chain Hilton wants to compare its growth to another benchmark company. What company should it compare itself to
Answers
Answer:
Marriott, an upscale hotel chain
Explanation:
the cost of capital depends primarily on the blank______ of funds, not the blank______.
Answers
The cost of capital depends primarily on the source of funds, not the use of funds.
The cost of capital depends primarily on the source of funds, not the use of funds. To explain further, the cost of capital is the rate of return that a company needs to earn in order to satisfy its investors or lenders. The source of funds can come from equity (e.g. stocks), debt (e.g. bonds), or a combination of both. Each source of funds has its own cost associated with it, such as interest payments on debt or dividend payments on equity. Therefore, the mix of equity and debt financing a company uses will affect its overall cost of capital. On the other hand, the use of funds refers to how a company invests its capital, such as in new projects or acquisitions. While the use of funds can impact a company's profitability, it does not have a direct impact on the cost of capital.
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INSTRUCTIONS
Develop a media strategy for 2023 For Lenovo Computers taking into account the media mix, seasoning, timing and the media budget.
When thinking about Lenovo Computers should advertise their products you need to take into consideration the different media channels to create an effective media mix (use at least 5 media channels in your proposal). The season when the campaign is launch is also very important and can change related to the category of product, link those concepts with a hypothetical budget and the timing and frequency of the campaign.
Number of Words: 1000
Word Document Required.
Answers
Developing a comprehensive media strategy is essential for Lenovo Computers in 2023 to reach its target audience effectively and drive brand awareness and sales.
In today's competitive market, a strong media strategy is crucial for any brand's success. Lenovo Computers needs to carefully consider the media mix, including television, online display advertising, social media marketing, influencer marketing, and print advertising, to ensure broad reach and engagement across different channels. The timing of the campaigns should align with peak seasons such as back-to-school and holidays, as well as new product launches to maximize impact. Allocating the media budget appropriately to each channel and maintaining a consistent presence will help Lenovo Computers connect with its target audience, build brand loyalty, and achieve its marketing objectives in 2023.
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Suppose the adult population in the country of Candora is 171 million. The number of adults in the labor force is 97 million, and the number of unemployed adults is 74 million. The labor force participation rate in Candora approximately equals _____.
Answers
Answer:
The labor force participation rate in Candora approximately equals 56.72%.
Explanation:
Given that the adult population of Candora is 171 million, of which 97 million are in the workforce and 74 million are unemployed, to obtain the percentage of participation in the workforce of said country we must carry out the following calculation:
171 = 100
97 = X
(97 x 100) / 171 = X
9700/171 = X
56.72 = X
Thus, the percentage of participation in the Candora workforce is 56.72% of the country's adult population, while the remaining 43.28% are unemployed.
A urvey howed that the average commuter pend about 26 minute on a one-way doorto-door trip from home to work. In addition, 5% of commuter reported a one-way commute of more than one hour (Bureau of Tranportation Statitic webite,January 12, 2004)
Answers
This survey provides a snapshot of the average amount of time commuters spend on their daily trips to and from work.
It indicates that the majority of commuters spend approximately 26 minutes on their one-way trips, but that a small percentage of commuters have significantly longer commutes of more than one hour. This could be due to a variety of factors such as living in rural areas with limited public transportation options or living in an area with heavy traffic.
Surveys used to gather data ask a specific set of people about their beliefs, actions, or knowledge. In order to gather information about a service, product, or process, a survey is described as the act of looking at a process or questioning a predetermined sample of people.
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Walter is in dire need of $482. Out of other alternatives, he decides to take a cash advance on his credit card. His credit card has a cash advance fee of 3.4%. How much is his advance fee?
Answers
Walter needs $482 in urgent, and his credit card has a cash advance fee of 3.4%. Hence, his advance fees would be 3.4% of $482 which is $16.39.
What does place when you obtain a cash advance?A cash advance is a loan that your credit card company provides. When you obtain a cash advance, you are borrowing funds from the available credit on your credit card. This loan must be repaid, and the amount transferred cannot be greater than the balance that is currently available on your credit card.
What dangers exist with cash advances?When you take out a cash advance, especially one for a sizable sum, your utilization rate may rise, which could lower your credit score. One of the risks of credit card cash advances is a lower credit score. Cash advance grace periods do not exist.
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alex measured the length of an item to be 3.9 cm. the actual length is 3.5 cm what is alex percent error ?
Answers
Answer:
11.42 %
Explanation:
The formula for calculating percentage error
percentage error = observed value - actual value x 100
actual value
Percentage error = 3.9- 3.5 x 100
3.5
Percentage error = 0.4 x 100
3.5
Percentage error =0.1142 x 100
Percentage error = 11.42 %
Profit as calculated from the profit equation can be challenging to predict because the ________ varies with the chosen price, and can also impact the variable costs through production efficiencies.
Answers
Demand for goods varies, profit as calculated from the profit equation can be challenging to predict because the quantity demanded varies with the chosen price, and can also impact the.
What is profits?Profit is the amount of money that is realized after a business transaction have been done.
The profits is the money left for the owner of the business for spending without necessarily affecting the business.
Therefore, profit as calculated from the profit equation can be challenging to predict because the quantity demanded varies with the chosen price, and can also impact the.
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12. The right to own a business is referred to as the right
Answers
Assume the economy is operating at a real GDP above full-employment real GDP. Classical economists would prescribe which of the following policies?
A) Nonintervention.
B) Fixed rule.
C) Contractionary.
D) Expansionary.
Answers
Assuming the economy is operating at a real GDP above full-employment real GDP, classical economists would prescribe a contractionary policy. So, the correct answer is C).
Classical economists believe in the concept of self-adjusting markets and the idea that the economy will naturally return to full employment in the long run.
In this situation, where the real GDP exceeds the full-employment level, classical economists would recommend taking measures to slow down the economy and reduce aggregate demand.
A contractionary policy typically involves actions such as reducing government spending, increasing taxes, and tightening monetary policy to curb inflationary pressures and bring the economy back towards its long-run equilibrium.
Therefore, the correct answer is C) Contractionary.
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According to the digital disconnect and the lecture, the global digital divide is the result of _____.
Answers
According to Digital Disconnect, the global digital divide is the result of the hyper-commercialization of Internet development that only serves affluent populations/groups.
The Digital Disconnect refers to experts' examination of current theory, research, and practice in socio-digital inequality. The Digital Disconnect provides a thorough analysis of capitalism's exploitation of the Internet. As per the Digital Disconnect, it is the hypercommercialism of mainstream computing technologies that causes the global digital divide. The global digital divide refers to global discrepancies, particularly between developing countries, and developed in access to computing and information resources such as the Internet, as well as the opportunities that such access provides.
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describe the benefits of having an electronic resume
Answers
Answer:
Online resumes offer more flexibility and room for creativity than their printed counterparts. Here are just a few benefits of using an online resume service: Undoubtedly, some of your skills and prior experiences are more relevant to some jobs/companies than others.
Explanation:
hope it helps
Once the affinity mapping exercise was complete, Imran looked at the totality of work. His team was responsible for multiple application modules: health information, finance, housekeeping, and human resources. Tracking all the user stories under a single project did not seem feasible, nor would it enable Imran to assess the performance of his team. Imran decided to use epics to represent each module for which his team was responsible. When he completed organizing the user stories into epics, Imran noticed some discrepancies with work distribution. He only had one resource assigned to the health information module, but the volume of work expected to be completed during the same period was more than that for Imran's other modules. Additionally, health information had a high number of medium to large stories. Imran questioned his vendor product owner. The product owner assured him that the work had been performed in previous projects at other organizations with the same work complement. Without his own empirical data, Imran decided to trust his product owner's input, but flagged it as a risk to his project sponsor. Once his team had completed a sprint, Imran would have more data to determine whether the resource risk was in fact an issue and would require corrective action. Why was Imran unable to confirm there was a resource risk with one of his modules? Explain your answer.
Answers
Imran couldn't confirm the resource risk without empirical data from his own project, and he planned to gather this data during the sprint to make informed decisions about the team's performance and potential corrective actions.
Imran was unable to confirm the existence of a resource risk with the health information module because he lacked empirical data specific to his own project. While he noticed discrepancies in work distribution and identified potential challenges such as having only one resource assigned to a module with a high volume of work, he relied on the assurance of the vendor product owner that similar work had been successfully performed in other projects.
Without his own empirical data, Imran couldn't conclusively determine if the resource allocation was problematic or if the vendor's claims were valid. To validate the resource risk, Imran needed to observe the actual performance of his team during the sprint. By tracking the progress of the health information module, he could gather empirical data regarding productivity, completion rates, and potential bottlenecks.
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How important is money
Answers
Answer:
very important
Explanation:
money is a global income source for everyone. we all have different types but it is all still money. now say one country got rid of money and had people pay for stuff using other things. if china did that lots of different countries wouldn't be able to get stuff from there unless they had so much of that product they could just give it up.
0. International Investment Projects [[] LO1] In the chapter opener, we mentioned Toyota's decision to invest $13 billion to increase production at five U.S. plants. Toyota apparently felt that it would be better able to compete and create value with U.S-based facilities. Other companies such as Fuji Film and Swiss chemical company Lonza have reached similar conclusions and taken similar actions. What are some of the reasons that foreign manufacturers of products as diverse as automobiles, film, and chemicals might arrive at this same conclusion?
Answers
Foreign manufacturers of diverse products like automobiles, film, and chemicals may decide to invest in U.S-based facilities due to reasons such as proximity to market, access to skilled labor, favorable business environment, and potential cost savings.
There are several reasons why foreign manufacturers from different industries may come to the conclusion of investing in U.S-based facilities. Firstly, proximity to the U.S. market can be advantageous in terms of reducing transportation costs and ensuring timely delivery of products to customers. Secondly, the United States offers access to a skilled labor force, which is essential for maintaining high-quality production standards and innovation. Thirdly, the U.S. business environment, including legal and regulatory frameworks, infrastructure, and support systems, can provide a favorable and stable operational environment for foreign manufacturers. Lastly, depending on specific circumstances, there may be potential cost savings related to factors such as raw materials, energy costs, or tax incentives that make investing in U.S-based facilities economically attractive for foreign manufacturers across various industries.
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The following information relates to
Longman, Inc.'s
overhead costs for the month:
1(Click
the icon to view the information.)
Requirements
1.
Compute the overhead variances for the month: variable overhead cost variance, variable overhead efficiency variance, fixed overhead cost variance, and fixed overhead volume variance.
2.
Explain why the variances are favorable or unfavorable.
Requirement 1. Compute the overhead variances for the month: variable overhead cost variance, variable overhead efficiency variance, fixed overhead cost variance, and fixed overhead volume variance.
Begin by selecting the formulas needed to compute the variable overhead (VOH) and fixed overhead (FOH) variances, and then compute each variance amount.
(Actual cost - Standard cost) × Actual hours
=
VOH cost variance
(Actual hours - Standard hours allowed) × Standard cost
=
VOH efficiency variance
Actual overhead - Budgeted overhead
=
FOH cost variance
Budgeted overhead - Allocated overhead
=
FOH volume variance
=
=
=
=
Requirement 2. Explain why the variances are favorable or unfavorable.
The variable overhead cost variance is
(1)
because
Longman
actually spent
(2)
than budgeted.
The variable overhead efficiency variance is
(3)
because the actual hours used was
(4)
than budgeted.
The fixed overhead cost variance is
(5)
because
Longman
actually spent
(6)
than budgeted for fixed overhead.
The fixed overhead volume variance is
(7)
because
Longman
allocated
(8)
overhead to jobs than the budgeted fixed overhead amount.
1: Data Table
Static budget variable overhead
$7,500
Static budget fixed overhead
$3,000
Static budget direct labor hours
1,500 hours
Static budget number of units
7,500 units
Longman
allocates manufacturing overhead to production based on standard direct labor hours. Last month,
Longman
reported the following actual results: actual variable overhead,
$10,100;
actual fixed overhead,
$2,840;
actual production of
7,200
units at
0.25
direct labor hours per unit. The standard direct labor time is
0.2
direct labor hours per unit
(1,500
static direct labor hours /
7,500
static units).
(1)
unfavorable
favorable
(2)
less
more
(3)
unfavorable
favorable
(4)
less
more
(5)
favorable
unfavorable
(6)
less
more
(7)
unfavorable
favorable
(8)
less
more
Answers
Variable overhead cost variance:Actual variable overheads = $10,100 ($1.41 per direct labor hour)Static variable overheads = $7,500 ($1.50 per direct labor hour)Variable overhead cost variance = (Actual variable overheads - Static variable overheads) x Actual direct labor hours
The variance analysis of Longman, Inc. overhead costs has been calculated, and it has been observed that the variable overhead cost variance is $630 Favorable, while the variable overhead efficiency variance is $540 Favorable. The fixed overhead cost variance is $160 Favorable, and the fixed overhead volume variance is $300 Unfavorable. The variance analysis indicates that the actual costs of Longman, Inc. are relatively lower than the budgeted cost for variable overheads and fixed overheads, which leads to a favorable variance.
On the other hand, it shows that Longman, Inc. allocated more overhead to jobs than the budgeted fixed overhead amount, which leads to an unfavorable variance.
In conclusion, the favorable variable overhead cost and efficiency variances and the favorable fixed overhead cost variance should be appreciated by the company as it implies cost savings, but the unfavorable fixed overhead volume variance indicates that Longman, Inc. needs to reassess its overhead allocation plan.
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A guidance counselor is:
o a. someone who works with students with disabilities.
o b. someone who oversees a student's academic progress.
o c. someone who oversees high school operations.
o d. someone who teaches classes and monitors hallways.
Answers
A guidance counselor is a person who works in the schools and check with the student's academic progress.
Who is a guidance counselor? Discuss his responsibilities?A guidance counselor are the certified professionals who are employed in the schools and different institutions.
They helps the students by giving them advise and consultancy about their career and academic growth.
They basically assess the student's ability and provides them with personal counselling.
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1.2 A business plan is a significant document in guiding
entrepreneurs. Develop a business of your choice and draw an
all-encompassing strategic business plan for your business.
for 18 marks
Answers
A business plan is a crucial document that provides guidance to entrepreneurs in developing and managing their businesses. It outlines the goals, strategies, and tactics necessary for the success of the business.
To create an all-encompassing strategic business plan, you should consider the following steps:
1. Executive Summary: Begin your business plan with a concise overview of your business idea, including the mission, vision, and objectives. This section should provide a high-level summary of the entire plan.
2. Company Description: Provide detailed information about your business, including its legal structure, location, products or services, target market, and competitive advantage. Explain how your business fills a gap or meets a need in the market.
3. Market Analysis: Conduct thorough research on your target market, including its size, demographics, purchasing behavior, and trends. Identify your competitors and analyze their strengths and weaknesses. This analysis will help you identify opportunities and potential challenges.
4. Organizational Structure and Management: Outline the organizational structure of your business, including the roles and responsibilities of key team members. Discuss your management team's qualifications and expertise, highlighting how their skills align with the needs of the business.
5. Product or Service Line: Describe your products or services in detail, including their features, benefits, and unique selling points. Explain how your offerings meet the needs and preferences of your target market.
6. Marketing and Sales Strategy: Develop a comprehensive marketing and sales plan. Identify your target customers, determine the best channels to reach them, and outline your pricing strategy. Describe your promotional activities, such as advertising, public relations, and digital marketing.
7. Operations and Logistics: Outline how your business will operate on a day-to-day basis. Discuss the facilities, equipment, and technology required to run your business efficiently. Include information on suppliers, distribution channels, and any outsourcing arrangements.
8. Financial Projections: Provide a detailed financial forecast for your business, including sales projections, expenses, and profitability. Include a cash flow statement, balance sheet, and income statement. Additionally, include a break-even analysis and discuss your funding requirements, if applicable.
9. Risk Assessment and Mitigation: Identify potential risks and challenges that your business may face, such as changes in market conditions, competition, or regulatory requirements. Develop strategies to mitigate these risks and discuss contingency plans.
10. Implementation Plan: Create a timeline and action plan for implementing your business strategies. Outline key milestones and deadlines, along with the tasks and responsibilities of team members.
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Is a business plan a one time fee?
Answers
Answer:
i think so :)
Explanation:
QUESTION 7 of 20: Your savings account pays 2.5% interest per year. How much interest does the account pay per month.
a) .02%
b) 04%
c) 21%
d) 43%
Answers
Answer:
a) .02%
Explanation:
One year has 12 months.
The interest rate per year = 2.5%
Interest earned per month will be
=2.5% / 12
=0.02%
Answer:
c 21%
Explanation:
i got it right
3. ______ are defined as goods or services that are required for health and safety.
Answers
Occupational Health and Safety are defined as goods or services that are required for health and safety. Information standards are guidelines governing the information that must be provided to consumers when they purchase specific goods.
What is the safety of goods?A safe product is one that delivers either no risk or a minimum tolerable level of risk, taking into account the product's typical or reasonably foreseeable use and the need to maintain a high level of consumer protection.
Occupational health and safety is a multidisciplinary discipline that deals with all elements of workplace health and safety, with a heavy emphasis on preventing workplace dangers.
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Sales tax in your community is 7.5%. If you go to Becks and buy a polar pop for $0.99, slice of pizza for $2.25, and chips for $0.75, what amount will you pay once the sales tax is added to your purchase?
Answers
Answer:
$4.29
Explanation:
Sales tax is a type of consumption tax. It is levied by the government or an agency of the government on the sales. Taxes increase the prices of goods and services
Total amount paid = total price of items purchased + tax amount
total price of items purchased = $0.99 + $2.25 + $0.75 = $3.99
Tax amount = 0.075 x $3.99 = $0.299
Total amount paid = $4.29
For both articles, what can you tell me about the values of Harvard and Entrepreneur?
Answers
The article referenced is "If you want to be an entrepreneur, don't go to Harvard.
What are the values of the Harvard Graduate viz a- viz that of the Entrepreneur?Regardless of the size of the organization, "Core Values" should be prioritized. Values direct the path of business, influencing strategy and decision making. Essentially, basic principles serve as the foundation around which we develop our firm. Core Values provides several advantages to the firm.
Students at Harvard have access to classes, research institutions, and faculty mentors from around the university. It's the ideal location to explore your favorite and yet-to-be-discovered academic interests, with world-renowned teachers, cutting-edge resources, and personalized training.
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Why should you understand what you can and cannot copyright?
Answers
Answer:
Copyright is important as it helps to protect the value of an author/academic/researchers work, by giving the originator of the work the ability to protect it from unlicensed or uncredited usage.
Explanation:
Answer:
So that therefore you wouldn't be fined of plagiarism of any kind.
Explanation: