For both questions given that : a21 b12 c14

A recent study in Country T reveals that the application of); hundred kilograms of' Fertilizer K and y hundred kilograms of Fertilizer N to a hectare of paddy Iield leads to an increase in rice production by approximately R|[:r, y] "KB, where R (I! I?) : ElU.1xlh3_1' {3.1. + I}: + 2y} . {a} Determine the optimal amount of Fenilizer K and N that should be applied to achieve the highest rice yield per hectare. Give your answer correct to the nearest kilograms. {6 marks} {b} Fertilizers K and N are both sold at S a per kg in Co untry T. The government of Country T offers a fertilizer subsidy of' S l per hectare to paddy farmers with the aim of bolstering the rice industry. Assuming that the entire fertilizer subsidy is dedicated to purchasing Fertilizer K and N. how should the money be allocated to maximize the rice production per hectare? Justify your answer by using the method of Lagrange multipliers. {4 marks}