Consider the 0-1 knapsack problem:{cjxj : Ëajxj;ajxjj=1with aj, c; > 0 for j = 1,..., n.(a) Show that if > ... > cn > 0, Σ' a; ≤ b and Σ';=1 a; > b, thesolution of the LP relaxation is xj = 1 for j = 1,...,r - 1,xp =a₁an(b- Σ;a;)/a,, and x; = 0 for j > r.(b) Solve the instancemaxxj ≤ b,x € (0,1)"}max 17x1 + 10x2 + 25x3 + 17x45x1 + 3x2 + 8x3 + 7x4 ≤ 12x = {0,1}4by branch-and-bound. Always branch first on the node with the bestbound. You must number the nodes as you explore them. Namethe first node as "Root". Create a table with one row for each node.At each row, indicate the value of the variables in the solution ofthe node, the capacity used, the profit of the solution (or indicateits infeasibility) and the status associated with the node (branched,pruned by infeasibility, pruned by integrality or pruned by quality).

Given information:The knapsack problem.with for To show:If The solution of the LP relaxation is

Answered: Consider the 0-1 knapsack problem: max…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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