4.(25 points) An agricultural producer has been asked by Ducks Unlimited to cons

Question

4.(25 points) An agricultural producer has been asked by Ducks Unlimited to consider setting aside part of the farm area as a "buffer strip" around a wetland area. The wetland is in the middle of the farm operation and is adjacent to the farm's productive area. The buffer strip would create a zone within which no agricultural production would take place The farm consists of 1000 hectares of land suitable for crop production (crop land) and 500 hectares of pasture land. The wetland is adjacent to both crop and pasture land. If used for agricultural production, the farmer can generate $100 in profit per hectare of crops and $25 per hectare of pasture. The farmer has set a target of $75,000 of profit from the farm For each hectare of crop land converted to buffer strip, the profit would become zero since there is no agricultural production allowed in that area. For pasture land converted to buffer strip, not only would there be no profit from agricultural production, the farmer would need to construct a fence to keep livestock out of that portion of the buffer strip area. The annual cost of the fence (considering construction and maintenance costs) is $15 per hectare, which means that the area converted from pasture to buffer strip would result in a negative profit per hectare. No fence is required for buffer strip created from crop l and. The farmer wishes to allocate all 1000 hectares of crop land to a combination of cropping and buffer strip area, and all 500 hectares of pasture land to a combination of pasture and buffer strip area. Ducks Unlimited has surveyed the farmer's wetland area and they are recommending that a total buffer strip area (i.e., the total from both crop and pasture land) of 450 hectares would be sufficient to adequately protect the wetland. Given this information, what land use plan would provide 450 hectares for a buffer strip and still meet the target of $75,000 in profit? Use matrix methods to obtain your answer Note for Question 4: Remember that the producer is deciding how many hectares to set aside for buffer strip from crop land and how many hectares to set aside from pasture land, as well as how many hectares to allocate to crop and pasture production

Explanation / Answer

Let's assume Crop land = C hectares

and Pasture Land = P hectares

Buffer land = B hectares

and given that Buffer strip = 450 heactare i.e. B = 450

We know that

Total land = B + P + C = 1000 + 500 = 1500

P + C = 1050

Land converted to buffer from pasture = 500 - P

Total profit = profit from pasture and crop - loss from converting pasture to buffer

75000 = 100(C) + 25 (P ) - 15 (500 -P)

75000 = 100C + 25P - 7500 + 15P

82500 = 100C + 40P

82500 = 60 C + 40(C + P ) = 60C + 40(1050) = 60C + 42000

40500 = 60C

C = 675 i.e. Crop land is 675 hectares

P = 1050 - 675 = 375 hectare for Pasture land

B = 450 hectare buffer strip

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