Question

Find two positive numbers x and y such that x + y = 60 and xy ^3 is maximum.

Answer 1

HELLO DEAR,

GIVEN:- x + y = 60
y = (60 - x)

and,

S = xy³ (maximum)

so, S = x(60 - x)³

dS/dx = x*3(60 - x)²(-1) + (60 - x)³*1

dS/dx = (60 - x)²(-3x + 60 - x)

dS/dx = (60 - x)²(60 - 4x)

for a maximum or minimus , we have (dS/dx) = 0.

now, dS/dx = 0

therefore, 0 = (60 - x)²(60 - 4x)

60 - x = 0 and (60 - 4x) = 0

x = 60 and x = 15

so, x = 60 , x = 15

y = 60 - 60 and y = 60 - 15

y = 0 and y = 45

hence, the no. are 15, 45

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Answer:

Step-by-step explanation:

Hope you understood.