Answer :
The BIP branch-and-bound algorithm is a method used to solve binary integer programming (BIP) problems. In this particular problem, we aim to maximize the objective function Z = 3x₁ + 3x₂ + 5x₃ - 2x₄ - x₅, subject to the constraint 1: x₁ + 2x₂ - 3x₄ - x₅ ≤ 15x₁ + 30x₂ + 35x₃ + 45x₄ + 45x₅ ≥ 50.
To solve this problem using the BIP branch-and-bound algorithm, we start by initializing an upper bound for the objective function value, Z_best, to a very low value. Then, we construct a node in the branch-and-bound tree, where we choose one variable to branch on. We create two child nodes, each representing one of the possible binary values for the selected variable. For each node, we evaluate the objective function value using the current binary assignments. If the node's objective function value is greater than Z_best, we update Z_best. If the node's linear constraints are satisfied, we have found a feasible solution. Otherwise, we continue branching on other variables until we have explored all nodes or determined that they are infeasible.
Through this iterative process of branching and bounding, we systematically explore the solution space and update the best objective function value until we reach an optimal solution or prove the problem to be infeasible. The BIP branch-and-bound algorithm provides a systematic approach to solve BIP problems, allowing us to find the maximum value of the objective function while satisfying the given constraints.
Learn more about binary here: brainly.com/question/32659188
#SPJ11
