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 represented by the shaded triangle in the graph. The vertices of the triangle are (1,2), (2,4), and (4,2).

To find the maximum and minimum of the objective function, we simply need to evaluate the function at each of the vertices and choose the largest and smallest values.

At (1,2), the objective function evaluates to 11.
At (2,4), the objective function evaluates to 28.
At (4,2), the objective function evaluates to 44.

Therefore, the maximum value of the objective function is 44, and it occurs at the point (4,2). The minimum value of the objective function is 11, and it occurs at the point (1,2).

So, the correct answer is D) max: 46, min: 11.

Use the Given Feasible Region Determined by the Constraint Inequalities