Source of problem list: https://web.tecnico.ulisboa.pt/mcasquilho/compute/_linpro/TaylorB_module_c.pdf

Problem 1

\begin{aligned} \max \quad & z = 5x_1 + 4x_2 \\ s.t. \quad & 3x_1 + 4x_2 \leq 10 \\ \quad & x_1, x_2 \geq 0, \text{integer} \end{aligned}

Problem 2

\begin{aligned} \min \quad & z = 3x_1 + 6x_2 \\ s.t. \quad & 7x_1 + 3x_2 \geq 40 \\ \quad & x_1, x_2 \geq 0, \text{integer} \end{aligned}

Problem 3

Example solution in source: ilp_branch_and_bound_textbook_excerpt.pdf [PDF]

\begin{aligned} \max \quad & z = 100x_1 + 150x_2 \\ s.t. \quad & 8{,}000 x_1 + 4{,}000 x_2 \leq 40{,}000 \\ \quad & 15 x_1 + 30 x_2 \leq 200 \\ \quad & x_1, x_2 \geq 0, \text{integer} \end{aligned}