This work introduces an extended model of the 0/1 Knapsack Problem, focusing on conflicts between items. The objective function of this problem not only considers the total profit of the selected items but also incorporates the maximum profit of the items in the knapsack as a bonus cost. We provide a mathematical formulation of the problem and propose a Fully Polynomial-Time Approximation Scheme (FPTAS) based on a pseudo-polynomial time dynamic programming algorithm.