Question

Find the maximum and minimum values of the function f(x,y,z)=y*z+x*y subject to the constraints y^2+z^2=1 and x*y=6


NOTE: I need a full work

Answer 1

since xy = 6 is the constraint

therefore f(x,y,z) = yz+xy = yz + 6

it is sufficient to maximize or minimize yz over y²+z²=1

maximum value is f(x,y,z) = yz+xy = yz + 6 = 6 + 1= 7

minimum value is f(x,y,z) = yz+xy = yz + 6 = 6 - 1 = 5

Answer 2

Since x*y = 6 is the constraint

therefore f(x,y,z) = y*z+x*y = y*z + 6

it is sufficient to maximize or minimize y*z over y^2+z^2=1

maximum value is f(x,y,z) = y*z+x*y = y*z + 6 = 6 + 1= 7

minimum value is f(x,y,z) = y*z+x*y = y*z + 6 = 6 - 1 = 5