Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of the feasible points.
-z = 2x + 3y. Find maximum and minimum.
A)maximum value: 37; minimum value: 4
B)maximum value: 37; minimum value: 6
C)maximum value: 19; minimum value: 4
D)maximum value: 19; minimum value: 6

Question

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of the feasible points.
-z = 2x + 3y. Find maximum and minimum. 
A)maximum value: 37; minimum value: 4 
B)maximum value: 37; minimum value: 6 
C)maximum value: 19; minimum value: 4 
D)maximum value: 19; minimum value: 6

Quizplus · Accepted Answer

By analyzing the graph, we can see that the maximum value of z is obtained at point (7,10) which is the corner point of the feasible region. Substituting the values of x and y in z, we get z= 2(7) + 3(10) = 37. Similarly, the minimum value of z is obtained at point (0,2) which is another corner point of the feasible region. Substituting the values of x and y in z, we get z= 2(0) + 3(2) = 6. Therefore, the maximum value of z is 37 and the minimum value of z is 6. The only choice that has these values is A. The maximum value of z (2x + 3y) can be found at the corner point (7, 10), where z = 2(7) + 3(10) = 37.
The minimum value of z (2x + 3y) can be found at the corner point (1, 1), where z = 2(1) + 3(1) = 5.
Therefore, the answer is A: maximum value: 37; minimum value: 4.

Find the Maximum or Minimum Value of the Given Objective