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Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum
Asked by Siddhant Last Modified
Answer 
Harshit Bhardwaj
Let one number be x. Then, the other number is y = (35 − x).
Let P(x) = x2y5. Then, we have:
x = 0, x = 35, x = 10
When x = 35,
and y = 35 − 35 = 0. This will make the product x2y5 equal to 0.
When x = 0, y = 35 − 0 = 35 and the product x2y2 will be 0.
∴ x = 0 and x = 35 cannot be the possible values of x.
When x = 10, we have:
∴ By second derivative test, P(x) will be the maximum when x = 10 and y = 35 − 10 = 25.
Hence, the required numbers are 10 and 25.
read less Abdul Shameeh Ap
Passionate Physics teacher (NIT Calicut graduate) with more than 4 years of teaching experience
Lourembam Devraj Singh
Science and Arts Home Tutor
X+Y =35
So, X= 35 - Y ... ..... .. Eqn 1
Product of X and Y = X x Y= (35-Y) Y = 35Y - Y^2
For product of them to be maximum, their derivative should be equated to zero.
Thus, d/dy (35y -y^2) = 0
Or, 35 - 2y= 0
Therefore, y=35/2= 17.5
And x = 35-y= 17.5
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