question_answer 77)

Find two positive number x and y such that x + y = 60 and xy3 is maximum. 

Answer:

P = xy3 = (60 ? y)y3 = 60y3 ? y4                         [Using (1)]                           Now             = 12 [30 × 45 ? 2025]       = 12 [1350 ? 2025] < 0       is maximum when y = 45       (1)             y = 45.