Question

can someone explain how to find two positive numbers such that the sum of the first and twice the second is 100 and their product is a maxium?

Answer 1

x+2y=100
=>x=100-2y...i

Now, P=x*y=(100-2y)*y=100y-2y^2

Answer 2

Now, u need to find the value of y for which P is maximum...
U know calculas?

Answer 3

From Mathematica:\[\text{Maximize}[\{x y,x+2y=100,x>0,y>0\},\{x,y\}] \]\[\{1250,\{x\to 50,y\to 25\}\} \]
A plot of 100y-2y^2 is attached.