Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints.
Objective function:

Z = 5x + 6y

Constraints:

X ≥ 0
Y ≥ 0
X + y ≥ 8
3x + 5y ≥ 30

A) No minimum
B) Minimum at (10, 0): 50
C) Minimum at (8, 0): 49
D) Minimum at (5, 3): 43
E) Minimum at (0, 8): 48

Question

Select the region determined by the constraints.Then find the minimum value of the objective function (if possible) and where it occurs, subject to the indicated constraints. ​
Objective function:
​
Z = 5x + 6y
​
Constraints:
​
X ≥ 0
Y ≥ 0
X + y ≥ 8
3x + 5y ≥ 30
​
A) No minimum 
B) Minimum at (10, 0): 50 
C) Minimum at (8, 0): 49 
D) Minimum at (5, 3): 43 
E) Minimum at (0, 8): 48

Quizplus · Accepted Answer

Graphing the constraints, we get a feasible region as shown in the image link below:
https://i.imgur.com/Xnt2eKj.png

Evaluating the objective function at the vertices of the feasible region:
Z(0,8) = 48
Z(10,0) = 50
Z(5,3) = 43
Z(0,0) = 0

Thus, the minimum value of the objective function occurs at (5,3) with a value of 43. Therefore, the answer is D.

Select the Region Determined by the Constraints