To find the vertices of the feasible region, we first graph the constraint x+y<7.
To graph this inequality, we can start by drawing the boundary line x+y=7, which is a straight line with a y-intercept of 7 and an x-intercept of 7. We can then shade the region below this line since the inequality is x+y<7, not x+y≤7.
The feasible region is the region that satisfies all the constraints of the problem. Since there are no other constraints listed, the feasible region is the shaded region below the line x+y=7.
To find the vertices of this region, we look for the points where the boundary line intersects the axes.
At x=0, y=7, so one vertex is (0,7).
At y=0, x=7, so another vertex is (7,0).
Therefore, the vertices of the feasible region are (0,7) and (7,0).