question_answer 78)

Find two positive numbers x and y such that their sum is 35 and the product x2 y5 is a maximum. 

Answer:

Given x + y = 35                        ?. (1)       Let P = x2y5 = (35 ? y)2 y5                                6125y4 + 7y6 ? 420y5 = 0        5y4 (875 + y2 ? 60y) = 0         y2 ? 60y + 875 = 0                 (y ? 25) (y ? 35) = 0        y = 25 and  as by (1),       x + y = 35 and x > 0.             = 7y3 [3500 + 6y2 ? 3000]             is maximum when y = 25 (1)        Required numbers are 10 and 25.