A farmer possesses 30 acre cultivated land that must be cultivated in two different mode of cultivations: organic and inorganic. The yield for organic and inorganic system of cultivations is 11 quintals/acre and 14 quintals/acre respectively. Using matrix method, determine how to divide 30 acre land among two modes of cultivation to obtain yields of 390 quintals. Which mode of cultivation do you prefer most and why?

Let farmer cultivates x acre by organic mode and y acre by inorganic mode.ATQ,11x+14y=390x+y=30We can write these equations in matrix form as,111411xy=39030-3011xy=-3030          R1R1-14R21011xy=1030          R1-13R11001xy=1020          R2R2-R1x=10 and y=20Therefore, farmer cultivates 10 acre by organic mode and 20 acre by inorganic mode.Inorganic cultivation gives more yield per acre land.Hence, we would prefer inorganic mode of cultivation.

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