Question 2 [It] marks]: A recent study in Country T reveals that the application ofx hundred kilograms of Fertilizer K and y hundred kilograms of Fertilizer N to a hectare of paddy eld leads to an increase in rice production by approximately R (I. y] \"Ha, where R (x, y] = el''lx'"'3-" [3x + a}! + 2):} . {a} Detem1ine the optimal amount of Fertilizer K and N that should be applied to achieve the highest rice yield per hectare. Give your answer correct to the nearest kilograms. {5 marks} {b} Fertilizers K and N are both sold at S a per kg in Country T. The goyemment of Country T offers a fertilizer subsidy of' S lt} per hectare to paddy f'amters with the aim of bolstering the rice industry. Assuming that the entire fertilizer subsidy is dedicated to purchasing Fertilizer K and N. honr should the money be allocated to maximize the rice production per hectare? Justify your answer by using the method of Lagrange multipliers. {4 marks}