Introduction to Calculus
Calculus
Level
2
Find two positive real numbers x and y such that their sum is 100 and their product is as large as possible. Express the answer as the product of x and y divided by 2.
The answer is 1250.
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1 solution
x+y = 100 Therefore, y= 100 - x
Let P be the product, then P= xy P= x(100-x) P= 100x - x^2
To find the two numbers, Set P'(x) = 0 and find x. P'(x)= 100 - 2x = 0 x= 50
Lastly, find the value of y.
y= 100-x = 100-50 = 50
(Express the answer as the product of x and y divided by 2)
xy/2 = 50(50)/2 = 2500/2 = 1250