Find two positive numbers whose product is 192 and the sum of the first and three times the second is a minimum.

Answer 1

x: 1st # y: 2nd # Minimize (x + 3y) under the constraint xy = 192. So y = 192/x

Minimize: (x + 576x^-1)

d/dx [x + 576x^-1] = 1 - 576/x² = 0

x² - 576 = 0

x = ± 24 , y = ± 8. But x, y > 0 , so 24 and 8 will minimize the expression.