Question

Maximize upper qequals3 xy squared, where x and y are positive numbers such that x plus y squared equals 3.

Answer 1

Answer:

Max Q = 27/4

Step-by-step explanation:

Maximize  Q = 3xy²

x and y are positive numbers   Such that

x + y² = 3

=> y² = 3 - x

Q = 3x(3 - x)

Q =  -3x² + 9x

differentiating with x

dQ/dx = -6x + 9

dQ/dx = 0

=> -6x + 9 = 0

=> x = 9/6

=> x = 3/2

dQ/dx = -6x + 9

d²Q/dx² = -6  < 0

=> Value of x will provide maximum value of Q

=> x = 3/2

y² = 3 - x =  3 - 3/2 = 3/2

Q = 3xy² = 3(3/2)(3/2)  = 27/4