Question

Maximize B=5xy^2, where x and y are positive numbers such that x=y^2=6.

Answer 1

Answer:

$B = 180$

Step-by-step explanation:

The numbers are:

$x = 6$ and $y = \sqrt{6}$

Finally, the value of B is:

$B = 5\cdot (6)\cdot (6)$

$B = 180$

Answer 2

Answer:

The maximum value of B is 45

Corrected question;

Maximize B=5xy^2, where x and y are positive numbers such that x+y^2=6.

The maximum value of B is _?

Step-by-step explanation:

Given that;

B = 5xy^2 ........1

And;

x + y^2 = 6

y^2 = 6 - x ........2

Substituting equation 2 to 1

B = 5x(6-x) = 30x - 5x^2

Maximizing B, at maximum point dB/dx = 0

dB/dx = 30 -10x = 0

30 = 10x

x = 30/10 = 3

x = 3

From equation 2;

y^2 = 6 - x = 6-3 = 3

y = √3

Maximum value of B is;

B = 5xy^2 = 5 × 3 × (√3)^2 = 45

B = 45

The maximum value of B is 45