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##### Part II, Problem 3 | Final Exam | CTL.SC1x Courseware | edX Part-(Answered)

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Part II, Problem 3 | Final Exam | CTL.SC1x Courseware | edX

Part II, Problem 3

You work for an agriculture supply company in Africa. Part of your job is to procure fertilizer for local small farmers in the area. Some problems with the fertilizer are that it must be ordered before the growing season begins, it has a very long lead-time, and the farmers need it only over a very short window of time. Additionally, the fertilizer cannot be stored for the next growing season, as it will deteriorate. So, you have to make the decision of how much fertilizer to order before the farmers in the local area have even determined how much of what crop to plant.

To make matters worse, you discover that no records were kept for the amount of fertilizer demanded by the farmers in the past. You have asked your customer farmers who have been there for decades and they tell you that typically they will collectively plant 210.0 acres. The fewest number of acres planted in a season that any farmer could remember was 190.0 acres while the most was 1080.0 acres. You decide to estimate the demand using a triangle distribution. You know that each acre of planted crop will require 41.0 pounds of fertilizer.

Fertilizer costs 0.22 $/pound and you sell the fertilizer to the farmers at 0.55$/pound. Additionally, you estimate that every pound of fertilizer you are short is equivalent to costing you 1 $/pound in loss of goodwill to the farmers that might translate into future loss of business. 3.1 How many pounds of fertilizer should you order if you wish to maximize profitability? Please round your answer to the nearest 100 pound. - unanswered 3.2 What Cycle Service Level (CSL) does your answer in 3.1 correspond to? Answer as a percentage with two decimals, without the percentage symbol. For instance, if your solution is 95.554%, you answer 95.55. - unanswered 3.3 When you tell a local manager about your plans, he asks you about the left-over fertilizer. He points out that, according to a recent law, fertilizer that is not sold need to be taken to a special destruction facility. Together you estimate that the cost associated with taking it to the facility is 0.5$/pound.

If you include a destruction cost of 0.5 $/pound in your calculations, how many pounds of fertilizer should you order if you wish to maximize profitability? Please round your answer to the nearest 100 pound. (Hint: Think of the destruction cost as a negative salvage value.) - unanswered 3.4 What Cycle Service Level (CSL) does your answer in 3.3 correspond to? Answer as a percentage with two decimals, without the percentage symbol. For instance, if your solution is 95.554%, you answer 95.55. - unanswered 3.5 You do some additional research and find a not-for-profit community plantation that is happy to receive any unsold fertilizer. They are even willing to come and pick it up, so donating left-over fertilizer comes at no cost to you. Rather, you believe it comes with a long-term goodwill benefit (revenue) as you will give back to the local community. You can safely assume the plantation will pick up all unsold fertilizer so that none has to be taken to the destruction facility. After hearing about the plantation, the local manager says: "That is great news! We should aim for a 95% service level since having too much in stock is costless!" Call the goodwill benefit from donating left-over fertilizer [mathjaxinline]g[/mathjaxinline]. What size of [mathjaxinline]g[/mathjaxinline] will make a 95% Cycle Service Level the profit optimizing Cycle Service Level? Answer with two decimals. - unanswered Check your answerSave your answer You have used 0 of 3 submissions ' data-progress_detail="0/5" data-progress_status="none" data-url="/courses/course-v1:MITx+CTL.SC1x_2+1T2016/xblock/block-v1:MITx+CTL.SC1x_2+1T2016+type@problem+block@a0724d02edd245c0a95559faef557aae/handler/xmodule_handler" data-problem-id="block-v1:MITx+CTL.SC1x_2+1T2016+type@problem+block@a0724d02edd245c0a95559faef557aae"> Part II, Problem 3 (5 points possible) You work for an agriculture supply company in Africa. Part of your job is to procure fertilizer for local small farmers in the area. Some problems with the fertilizer are that it must be ordered before the growing season begins, it has a very long lead-time, and the farmers need it only over a very short window of time. Additionally, the fertilizer cannot be stored for the next growing season, as it will deteriorate. So, you have to make the decision of how much fertilizer to order before the farmers in the local area have even determined how much of what crop to plant. To make matters worse, you discover that no records were kept for the amount of fertilizer demanded by the farmers in the past. You have asked your customer farmers who have been there for decades and they tell you that typically they will collectively plant 210.0 acres. The fewest number of acres planted in a season that any farmer could remember was 190.0 acres while the most was 1080.0 acres. You decide to estimate the demand using a triangle distribution. You know that each acre of planted crop will require 41.0 pounds of fertilizer. Fertilizer costs 0.22$/pound and you sell the fertilizer to the farmers at 0.55 $/pound. Additionally, you estimate that every pound of fertilizer you are short is equivalent to costing you 1$/pound in loss of goodwill to the farmers that might translate into future loss of business.

3.1

How many pounds of fertilizer should you order if you wish to maximize profitability? Please round your answer to the nearest 100 pound.

3.2

What Cycle Service Level (CSL) does your answer in 3.1 correspond to? Answer as a percentage with two decimals, without the percentage symbol. For instance, if your solution is 95.554%, you answer 95.55.

3.3

When you tell a local manager about your plans, he asks you about the left-over fertilizer. He points out that, according to a recent law, fertilizer that is not sold need to be taken to a special destruction facility. Together you estimate that the cost associated with taking it to the facility is 0.5 $/pound. If you include a destruction cost of 0.5$/pound in your calculations, how many pounds of fertilizer should you order if you wish to maximize profitability? Please round your answer to the nearest 100 pound. (Hint: Think of the destruction cost as a negative salvage value.)

3.4

What Cycle Service Level (CSL) does your answer in 3.3 correspond to? Answer as a percentage with two decimals, without the percentage symbol. For instance, if your solution is 95.554%, you answer 95.55.

3.5

You do some additional research and find a not-for-profit community plantation that is happy to receive any unsold fertilizer. They are even willing to come and pick it up, so donating left-over fertilizer comes at no cost to you. Rather, you believe it comes with a long-term goodwill benefit (revenue) as you will give back to the local community. You can safely assume the plantation will pick up all unsold fertilizer so that none has to be taken to the destruction facility.

After hearing about the plantation, the local manager says: "That is great news! We should aim for a 95% service level since having too much in stock is costless!"

Call the goodwill benefit from donating left-over fertilizer g

Paper#9210834 | Written in 27-Jul-2016

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