Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist).
A) max: 110, min: 24
B) max: 52, min: 11
C) max: 11, min: 17
D) max: 46, min: 11
E) do not exist

Question

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the given objective function (if they exist). ​  ​  ​
A) max: 110, min: 24 
B) max: 52, min: 11 
C) max: 11, min: 17 
D) max: 46, min: 11 
E) do not exist

Quizplus · Accepted Answer

The feasible region is a polygon with vertices at (0,0), (4,0), (3,3), and (0,5). Evaluating the objective function at these vertices, we get:

(0,0): f(0,0) = 0
(4,0): f(4,0) = 20
(3,3): f(3,3) = 27
(0,5): f(0,5) = 25

Therefore, the maximum value of the objective function is 27 and the minimum value is 0. The option with these values is D.

Use the Given Feasible Region Determined by the Constraint Inequalities