find the maximum and the minimum values (if they exist) of the objective function z=3x+4y on the region bounded by: 2x+y>=5 x+5y>=16 2x+y<=14 -x+4y<=20 Solution The region bounded by the above 4 inequations (constraints) is the closed polygon ABCDA where A=(0,5), B=(1,3), C=(6,2) and D=(4,6). The values of the objective function z = 3x+4y at extrem points are as At A(0,5), z = 20 At B(1,3), z = 15 At C(6,2), z = 26 At D(4,6), z = 36 Therefore Max z = 36 and Min z = 15.

1. find the maximum and the minimum values (if they exist) of the objective function z=3x+4y on
the region bounded by: 2x+y>=5
x+5y>=16
2x+y<=14
-x+4y<=20
Solution
The region bounded by the above 4 inequations (constraints) is the closed polygon ABCDA
where A=(0,5), B=(1,3), C=(6,2) and D=(4,6).
The values of the objective function z = 3x+4y at extrem points are as
At A(0,5), z = 20
At B(1,3), z = 15
At C(6,2), z = 26
At D(4,6), z = 36
Therefore Max z = 36
and Min z = 15