Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 19H / c / Solution

Put $y_i=1-x_i$. Feasibility gives $y_i\ge 0$ andwhile the objective isTo maximize it, the required total deficit $1/2$ must be assigned entirely to the cheapest variable $y_1$. Thusand the unique optimizer isThis is the vertex $A$ from part (b).