Find two numbers x, and y that add to 30, and for which 2x^2 +5y^2 is a minimum.

Answer 1

x+y = 30 or y = 30-x

let S = 2x^2 + 5y^2
= 2x^2 + 5(30-x)^2
= 2x^2 + 4500 - 300x + 5x^2
= 7x^2 - 300x + 4500
dS/dx = 14x - 300
= 0 for a max/min
x = 300/14 , sub into y = 30-x