In Exercises
2
1
-
2
4
, the region of possible solutions is not bounded: thus, there may not be both a maximum and a minimum. After graphing the region of possible solutions and finding each corner point, you can determine if both a maximum and a minimum exist by choosing two arbitrary values of
z
and graphing the corresponding lines, as discussed in the section “Why the Corner Principle Works.”
The objective function
z
=
3
x
+
4
y
is subject to the constraints
2
x
+
y
≥
10
3
x
+
y
≥
12
x
≥
0
and
y
≥
0
Find the following.
a. The point at which the maximum occurs (if there is such a point)
b. The maximum value
c. The point at which the minimum occurs (if there is such a point)
d. The minimum value.