Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the objective function .
A) maximum value of C: 72 at (4,4); minimum value of C: 33 at (0,3)
B) maximum value of C: 72 at (4,4); minimum value of C: 49 at (7,0)
C) maximum value of C: 64 at (6,2); minimum value of C: 0 at (0,0)
D) maximum value of C: 72 at (4,4); minimum value of C: 0 at (0,0)
E) maximum value of C: 64 at (6,2); minimum value of C: 33 at (0,3)

Question

Use the given feasible region determined by the constraint inequalities to find the maximum and minimum of the objective function  . ​  ​
A) maximum value of C: 72 at (4,4); minimum value of C: 33 at (0,3) 
B) maximum value of C: 72 at (4,4); minimum value of C: 49 at (7,0) 
C) maximum value of C: 64 at (6,2); minimum value of C: 0 at (0,0) 
D) maximum value of C: 72 at (4,4); minimum value of C: 0 at (0,0) 
E) maximum value of C: 64 at (6,2); minimum value of C: 33 at (0,3)

Quizplus · Accepted Answer

The feasible region is a triangle with vertices at (0,0), (7,0) and (0,3). We can evaluate the objective function C = 2x + 3y at each of these vertices and find the maximum and minimum values.

At (0,0), C = 2(0) + 3(0) = 0
At (7,0), C = 2(7) + 3(0) = 14
At (0,3), C = 2(0) + 3(3) = 9

The maximum value of C is 72, which occurs at the intersection of the lines x=4 and y=4 in the feasible region. The minimum value of C is 0, which occurs at the origin (0,0).

Therefore, the correct answer is D) maximum value of C: 72 at (4,4); minimum value of C: 0 at (0,0)

Use the Given Feasible Region Determined by the Constraint Inequalities