5.(20) Consider a binary knapsack problem constraint $2x_1 + 3x_2 + 3x_3 + 5x_4 + 7x_5 + 11x_6 \le 15$, $x_j$
binary j = 1,..., 6. After solving the LP relaxation of the binary knapsack problem (with some
objective function), we obtained a fractional optimal solution $x^* = (1, 1, 0, 0.6, 1, 0)$.
(a)(10) Explain the problem we need to solve to identify a cover inequality violated by the current
solution $x^*$. Show your reasoning.
(b)(10) In addition, solve the problem by inspection and identify a cover inequality. What is the
criterion to determine whether the obtained cover inequality is violated by the solution $x^*$ or not?