Problem involving productivity

So, in summary, the productivity of Napier Grass is 40 tons per hectare per year while eucalyptus wood has a productivity of 10 tons per hectare per year. Napier Grass has a 6-month production cycle compared to the 6-year production cycle of eucalyptus wood. In order to obtain the same quantity of dry mass of eucalyptus wood after its first production cycle, an area S that is 48 times larger than the area R planted with Napier Grass is needed due to the smaller production cycle of Napier Grass.
  • #1
pc2-brazil
205
3
Problem involving productivity and area for planting

Homework Statement



Napier Grass has a productivity of about 40 tons of dry mass per hectare per year, which is, for example, at least four times greater than the productivity of eucalyptus wood.
Besides that, it has a 6-month production cycle, while the first cut of eucalyptus wood is done after six years.
Consider a region R, planted with Napier Grass, maintaining constant productivity. If one wants to obtain the same quantity, in tons, of dry mass of eucalyptus, after its first production cycle, it is necessary to plant an area S. What is the relation between S and R?

2. The attempt at a solution

Data:
Productivity of Napier Grass: 40 tons/ha/year
Productivity of eucalyptus wood: 10 tons/ha/year
Napier Grass production cycle: 6 months
Eucalyptus wood production cycle: 6 years
Attempt at a solution:
The quantity of Napier Grass produced in one year in the area R (ha) should be: 40R tons.
(I don't see how the production cycle of Napier Grass is important here, since, in 6 months, the amount produced should simply be 20R tons)
Then, in one eucalyptus production cycle, which is 6 years, the quantity of Napier Grass is: 40R*6 = 240R tons.
In 6 years, the quantity of eucalyptus produced in the area S should be 60S ton (since its productivity is 10 ton per hectare per year).
Since the quantities need to be the same:
60S = 240R
S = 4R
But the correct answer is S = 48R. I don't understand why. I think it has something to do with the different production cycles, but, as I already explained above, I don't see how.

Thank you in advance.
 
Last edited:
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  • #2


You have to look after what "productivity" means really. If it means the product during a single harvest per hectare, you get the given answer as result.


ehild
 
  • #3
OK, I get it now.
The smaller production cycle reduces the area needed for planting.
 

1. What is productivity and why is it important?

Productivity refers to the efficiency with which resources (such as time, money, and labor) are utilized to produce goods or services. It is important because it directly affects the output and profitability of a company or organization.

2. How can productivity be measured?

Productivity can be measured in various ways, depending on the industry and specific goals. Some common measures include output per hour, revenue per employee, and sales per square foot.

3. What are some common causes of low productivity?

There are several factors that can contribute to low productivity, such as outdated technology, inefficient processes, inadequate training, and poor communication among team members.

4. How can productivity be improved?

Productivity can be improved by identifying and addressing the root causes of low productivity, implementing efficient systems and processes, providing adequate resources and training, and promoting a positive work culture.

5. What are the potential benefits of increased productivity?

Increased productivity can lead to higher profits, improved quality of products or services, better customer satisfaction, and overall growth and success for a company or organization.

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