Homework SourseThe sum of two numbers is 216 How should the numbers be chos
The sum of two numbers is 216. How should the numbers be chosen so that the product of the first number squared and the second number is maximized?
Can someone please help me set up the problem and work it out. I am completely lost and have not idea where to start
Can someone please help me set up the problem and work it out. I am completely lost and have not idea where to start
Solution
x + y = 216
y = 216 - x
f(x) = x2 * y
= x2(216-x)
= 216 x2 - x3
f \'(x) = 216 * 2 x - 3x2
f\'(x) =0
3x2 - 432 x = 0
x = 432/ 3 = 144
f \"(x) = 432- 6x
substitute x= 144 we get f \"(x) = negative
so x = 144 is maximum
thus, value of x = 144 and y = 216 - 144 = 72
