Question

Find the maximum and minimum values of the function
f
(
x
,
y
,
z
)
=
3
x
−
y
−
3
z
subject to the constraints
x
2
+
2
z
2
=
289
and
x
+
y
−
z
=
−
5
. Maximum value is , occuring at (, ,). Minimum value is , occuring at (, ,).