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Find two positive numbers and such that their sum is 35 and the product x2y5 is a maximum

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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...
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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.

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Passionate Physics teacher (NIT Calicut graduate) with more than 4 years of teaching experience

x=11, y=24
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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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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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Related Questions

For all real values of x, the minimum value of  is

(A) 0 (B) 1

(C) 3 (D)

Let ∴By second derivative test, f is the minimum at x = 1 and the minimum value is given by . The correct answer is D.
Chiranjeevi
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