Final answer:
The maximum value of x + y under the given conditions can be found by graphing the lines 2x + y = 8 and x + 2y = 10, identifying the vertices of the feasible region, and evaluating x + y at each vertex to find the highest value.
Step-by-step explanation:
The conditions x ≥ 0, y ≥ 0, 2x + y < 8, and x + 2y < 10 define a set of linear inequalities that create a feasible region on the coordinate plane. This feasible region is the intersection of the half-planes defined by each inequality and is likely to be a bounded polygon. Since x and y are non-negative, we are restricted to the first quadrant. To find out if the expression x + y has a maximum value, we should look for the corner points of the feasible region.
By graphing the lines 2x + y = 8 and x + 2y = 10, we can find the intersection points by solving the system of equations. These points, together with the axes intercepts, form the possible vertices of our feasible region. The maximum value of x + y under these conditions will occur at one of these vertices, according to the theory of linear programming. To determine this maximum value, we simply evaluate x + y at each vertex and choose the largest result.