Question #41782

This question tests the Corner Point Method on a feasible region bounded by piecewise linear functions (modulus).

The specific trap is that students often assume the optimal solution in linear programming must lie at the intersection of the distinct constraint equations (i.e., where the upper and lower boundaries meet).

By doing so, they only find the intersection points $(2, 1)$ and $(-3, 0)$, leading to an incorrect maximum of 11.

However, the modulus functions introduce non-differentiable 'cusps' which act as hidden vertices of the feasible region.

The true maximum lies at the cusp $(1, 4)$ of the upper boundary, which requires explicit geometric piecewise analysis to identify, effectively punishing students who blindly solve $y_1 = y_2$ without graphing or analyzing the critical points of the absolute value terms.