Optimal Strategy for Solving a Special Case of the Knapsack Problem by the Branch and Bound Method

A particular case of the knapsack problem is considered for which the weights of all items are identical and the costs of the items take just two different values. The solution strategy of the knapsack problem by the branch and bound method is understood as the method for selecting the next subproblem from the list of subproblems treated in the course of the solution process in conjunction with the method for selecting the variable to decompose the selected subproblem if it is necessary to perform this decomposition. For the considered particular case of the knapsack problem, the optimal strategy of this case solution by the branch and bound method is found.