Find two positive numbers that satisfy the given requirements: The product is 147 and the sum of the first number plus three times the second number is minimum

Answer 1

x y = 147 so x = 147/y

x + 3 y = a

147/y + 3 y = a

da/dy = 0 for max or min = 3 -147/y^2

y^2 = 147/3 = 49

y = 7
x = 147/7 = 21 so x = 21 and y = 7