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Math Problem
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Case Analysis: Additional Question (Math Problem Sample)

Instructions:

How much orange juice concentrate can be processed in one 8-hour workday?

 

There is a bottleneck in the juice filtration process requiring half an hour for the filter change

= [8 hours-(1/2 set up* 4 filter set ups)]* 18,000 pounds per hour

=108,000 pounds per day

 

1b. Assume extraction had previously been setup for the size oranges being processed. How much idle time will there be in the extraction operation during one 8-hour workday?

 

If the extraction process followed the same schedule as the extraction process then would be need to shut down the operations for 30 minutes before it is restarted after having ran for 90 minutes.

 

The idle time= time for the filter setups for the 8 hour working day

= 0.5 hours* 4 filter setups/day= 2 hours/day

 

2a. If you could add storage capacity somewhere between steps two and four in this production line in order to increase daily output, where would you place it? How much storage would you add?

 

The ideal situation is to place the storage unit between filtration (3) and concentration (4) with a capacity of 3,000 pounds given that the production time differs from process to process between the two processes and so is the speed of movement.

 

At the time of filtration, this is 90/60*(20,000-18, 000)=3000.

 

2b. Why?

 

The need for the storage is that it helps in separating one phase to the other while also improving the overall performance of the system. The storage will not increase the speed of the concentrator, but will improve the downtime processes.

 

 Bottlenecks along with production timeline as well as the maximum capacity for a day influence decisions on choosing any of the options.

 

3a- If the cost of adding storage was $30/pound and the cost of reducing setup time by 50% using additional fixtures was $20,000 for the filter process and $10,000 for the extraction process, what action would you recommends in order maximizing the output of this production line?

 

The extractor deals with one type of juice and having lesser set up time will have no effect on the production process. The production is dependent on the filtration set ups as well as the production in the concentration phase.

 

To increase the capacity, the company can increase the storage capacity, reduce the set up time by 50% alone or increase the storage capacity and reduce the filter set up time by 50% simultaneously.

 

3b. How much will your recommended improvement(s) cost? How much additional capacity do you create?

 

•             If the amount in filtration is 20,000 pounds per hour this is then 30,000 pounds per 90 minutes

•             In the case of 18, 000 pounds per hour in the concentration phase is 27,000 per 90 minutes

•             Filtration: 30, 000 pounds/ 90 min

•             Concentration: 27,000 pound/ 90 min

•             Excess in filtration is 3,000 pounds/ 90 minutes

•             Additional storage capacity required is for 3,000 lbs

 

 The cost implication=$30/ lbs*3000lbs=$90,000+ $ 20,000=$ 110,000

 

PART B

Assume that the production system was running three sizes of oranges: large, medium and small in equal amounts every week. Furthermore, assume that Natural Blends requires that each orange size be processed at least once per day, but that as long as equal amounts of all three sizes were processed during a week, equal amounts of all three sizes do not need to be processed on any single day. Again, consider just the process steps of extraction, filtration and concentration and assume none of the improvements you recommended in Part A (Question 3) have been implemented.

                                  (2)                                   (3)                                                  (4)

 

 

4a. How often during an 8-hour workday would you have a setup change in the extraction process (e.g., how often would you changeover to another size of orange)?

120,000/ 20/000= 6 hours

 

There is a difference of 2 hours being [8 hours-6 hours]

At 2 hours with 20 minutes set up time= 2 hours/ 20 minutes= 120 mins/20mins= 6 times

 

4b. Why?

The minimum set-up time is two times and maximum is six times during the extraction process.

 

4c.What quantity of oranges of a particular size would you process before switching to another size?

 

In one hour the minimum production is 20,000 pounds.

The maximum production is 20,000 pounds * 4 hours being $80,000.

 

4d.What was the total amount of juice concentrate you can process through the three process steps (two through four) in one 8-hour workday?

 

Based on the assumption that there is no waiting time then, the juice processed is (20,000 pounds *6) being 120,000 pounds.

Non the other hand when waiting then it is (4*20,000)+ (0.5*20,000)=80,000+10,000     = 90,000 pounds.

 

 

 

 

PART C

 

5] How much time does it take for the blending operation to process one 8,000-pound order from Company A?

 

24,000 pound orders, and there is a 40 minute set up for the blending phase

Then 8,000/22,000*60 mins= 21.81 minutes

21.81 min+40min=61.8 min

 

6a. Which set of contracts in Table A would you recommend that Natural Blends accept?

 

I would choose option B and C

 

6b. Why?

The two options total to 648,000 being (18* 16,000) and (15* 24,000)

 

7] Once again, management was considering improvements but this time to the entire system. Which of the following improvements would you recommend to maximize the output of this plant? Why?

 

a)            Adding storage between process steps 2, 3 or 4, at a cost of $30 per pound

b)            Reducing the extraction changeover time from 20 minutes to 10 minutes at a cost of $10,000

c)             Reducing the filtration setup time from 20 minutes to 10 minutes at a cost of $20,000

d)            Reducing the blending setup time from 40 to 30 minutes at a cost of $50,000

source..
Content:

Case Analysis: Natural Blends
Name
Course: MGT 285
Instructor
Date
Additional questions
Filtration does not shut down for 30 minutes for every 90 minutes of operation, but runs continuously like the other stages.
Similar to the previous case the bottleneck is at the concentration stage where there is 18,000 pounds/ hour. Compared the previous case, there are no interruptions, earning that there is a higher capacity to process the process. The Natural Blends capacity is related to the quantity of the juice concentrate. Hence, there is a need to consider the maximum capacity for a day, bottlenecks and the production time line. The cycle time is dependent on the time that a task is completed from the start to the finish, taking into account the changeovers in between the process flow.
Extraction: 30,000 pounds/ 1.5 hours= 20,000 pounds/ 1 hr
Filtration: 30,000 pounds/ 1.5 hours= 20,000 ...
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