Unit 1.4. Family farm model – step 3

You modelled the problem below in steps 1 and 2 (or you can download it here modelEco_familyFarm_2.zip) :

« A farmer owns 5 ha of land. His family can provide the equivalent of 5 people per year in terms of working time. The number of working days per year and per person is estimated at 100. This farmer can choose between 4 agricultural activities whose costs, yields and prices are shown in the table below. The currency is the rupee.

ACTIVITIES Wheat Rice Sugar cane Livestock
YIELD
(Tons/ha or
Rupees/ha for livestock)
9 6 18 17000
COSTS (Rupees/ha) 3120 5480 11360 5000
PRICE(Rupees/ton) 990 3276 1686 1

For livestock, the value shown in the yield line directly measures the gross product per hectare. A value of 1 was therefore provided in the price line.

The table below compiles the resource needs for each activity.

ACTIVITIES Wheat Rice Sugar cane Livestock
Labour(days/year/ha) 40.5 96 282 159
Water (m3/ha) 740 3000 2200 1100
Land (ha) 1 1 1 1

The objective of the farmer is to maximize the global gross margin. The State decides to pass a law concerning water consumption and that it is now limited to 3000 m3 per farm. »

It is now possible to buy irrigation water.

We remind you that the dual value of water is 2.62 rupees. How much should 1 m3  of water cost so as to encourage the farmer to buy water ?

Modify the model in order to introduce the possibility of buying irrigation water at 2 rupees per m3.

If you need help and/or to make sure you use the same name for the data : 

How great is the land area dedicated to wheat (in ha) ? Round off to a hundredth.

How great is the land area dedicated to rice (in ha) ? Round off to a hundredth.

How great is the land area dedicated to sugar cane (in ha) ? Round off to a hundredth.

How great is the land area dedicated to livestock (in ha) ? Round off to a hundredth

How many m3 of water are bought ? Round off to the nearest unit.