A farmer possesses 30 acre cultivated land that must be cultivated in two different mode of cultivations: organic and inorganic - Maths - Determinants

Question

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?

Ashwini Kumar · Accepted Answer

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          R1→R1-14R2⇒1011xy=1030          R1→-13R1⇒1001xy=1020          R2→R2-R1⇒x=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