Find the maximum andor minimum values of the objective funct

Find the maximum and/or minimum value(s) of the objective function on the feasible set S. (If an answer does not exist, enter DNE.) Z = 4x - y

The feasible region determined by the constraints is shown:

The four vertices are A=(2,2) ; B=(10,1) ; C=(2,6) ; D=(7,9)

To find the maximum or minimum values of Z evaluate Z at each point:

At A=(2,2) Z = 4x-y = 4(2) - 2 = 8 - 2 = 6

At B=(10,1) Z = 4x-y = 4(10) - 1 = 40-1 = 39

At C=(2,6) Z = 4x-y = 4(2) - 6 = 8 - 6 = 2

At D=(7,9) Z = 4x-y = 4(7) - 9 = 28-9= 19

Hence the Z is maximum at (10,1) and the maximum value is 39

and Z is minimum at (2,6) and the minimum value is 2