Final answer:
The global extreme values of the function f(x,y)=7x−5y, within the constraints given, will be found by evaluating the function at the vertices of the polygon defined by the inequalities. The maximum and minimum will occur at one of these vertices.
Step-by-step explanation:
The student is looking to determine the global extreme values of the function f(x,y)=7x−5y within a certain region defined by the inequalities y≥x−9, y≥−x−9, and y≤8. To find the global extremes, we need to evaluate the function at the vertices of the region formed by the intersection of these inequalities, which are the feasible region's corners.
The global maximum and minimum will occur at one of these vertices since f(x, y) is a linear function and the region is a convex polygon.
By plotting the inequalities on a graph, we can identify the vertices of the polygonal feasible region and then evaluate the function f(x,y) at each vertex to find the extreme values.
The graph would be labeled with the function f(x) and the variable x, and the axes would be scaled with the maximum x and y values as detailed in the student's question. Since this is a planar problem involving inequalities and linear functions, it could also be solved using linear programming techniques.