Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.
-z = 9x + 10y. Find minimum.
A)minimum: 56
B)minimum: 57
C)minimum: 68
D)no minimum

Question

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points. 
-z = 9x + 10y. Find minimum.
A)minimum: 56 
B)minimum: 57 
C)minimum: 68 
D)no minimum

Quizplus · Accepted Answer

The optimal solution can be found at the corner point of the feasible region that minimizes the objective function. In this case, the corner point with the smallest z-value is (4,2) which gives a minimum of 9(4) + 10(2) = 56. Therefore, the minimum value of the objective function is 56, and the answer is A. Based on the graph, the feasible region is bounded below by the line y = 2x + 8. Thus, the minimum value of the objective function z = 9x + 10y is achieved at the point where this line intersects the line z = 9x + 10y. Solving the system of equations gives x = 4 and y = 16, which corresponds to a minimum value of z = 9(4) + 10(16) = 56. Therefore, the answer is (A) minimum: 56.

Find the Maximum or Minimum Value of the Given Objective