Assess students' ability to model and solve a constrained optimization problem: given a fixed outer rectangular fence, select inner planting rectangle dimensions and equal-width surrounding paths to maximize plantable area while meeting a fixed outer perimeter and a material-cost constraint for paths; students must draw a labeled diagram, formulate the linear equations and inequalities representing perimeter, path width, areas and cost, solve algebraically (or with simple linear programming) for the optimal dimensions, and justify the solution and reasoning.