Approximation for- Knapsack Problemswith Multiple Constraints

in this paper, the approximation for four kinds of knapsack prob- lems with multiple constraints is studied: 0/1 Multiple Constraint Knapsack Problem(0/1 MCKP), Integer Multiple Constraint Knapsack Problem (Integer MCKP), 0/1k-Constraillt Knapsack Problem (0/1 k-CKP) and Integer k-Constraint KnapsackProblem (Integer k-CKP). The following results are obtained:1) Unless NP = co - R, no polynomial time algorithm approximates 0/1 MCKPor Integer MCKP within a factor k(1/2)- for any > 0; unless NP = P, nopolynom…