Then enter the optimal solution of items for the knapsack with W = 8. For example, enter (2, 5), (4, 7) if those two items are selected What's the total value for fractional knapsack problem with W = 8? For example, enter 12.5 if the total value of selected items is 12.5
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- Consider given 3-CNF-SAT, apply the reduction steps of NP complete to clique and prove that 3 CNF sat is suitable (step by step solution) (x1 V x2 V x3) A (x1 V x2 V x3) A (x1 V x2 V x3) A (x1 V x2 V x3)Find an optimal solution to the fractional knapsack problem for an Instancewith number of items 5, Capacity of the sack W=10, profit associated with the items (p1,p2,p3,p4,p5)= (20,5,15,10,30) and weight associated with eachitem (w1,w2,w3,w4,w5)= (2,3,5,7,8).Consider 7 items along their respective weights and values I = I1, I2, I3, I4, I5, I6, I7W = 2,3,5,7,1,4,1V = 10,5,15,7,6,18,3 The capacity of knapsack W=15. Find the optimal solution of the fractional knapsackproblem. What is the complexity of finding the solution of fractional knapsack problem?
- . Find an optimal solution to the fractional knapsack problem for an instancewith number of items 5, Capacity of the sack W=15, profit associated withthe items (p1,p2,…,p5)= (15,7,6,18,3) and weight associated with each item(w1,w2,…,w7)= (2,3,5,7,4, ).Consider a knapsack problem with three items. Assume thatbenefits obtained if item i is chosen (ci ) are 4, 5, 7;amounts of the available resource used by item i (ai) are 6, 7, 8; and total amount of an available resource (b) is 13 Formulate an IP model for your problem. Please define decision variables, the objective function, constraints, and sign restrictions (if any).knapsack problem: given the first table: c beeing value and w beeing weight, W max weight. I got table 2 as a solution to: 2 Solve the Knapsack problem with dynamic programming. To do this, enter the numbers Opt[k,V ] for k = 1,...,5 and V = 1,...,9 in a table. Here Opt[k, V ] is the partial solution obtained for the first k items with maximum weight V. " Can somebody explain me the values of the table? How do they get calculated? Also how do i solve the followup-task: Using the values in the table, determine a solution OPTSOL(I)=(β1,β2,β3,β4), starting with β4. (Use backtracing to do this)
- please solve step py step no code . Find an optimal solution to the fractional knapsack problem for an instancewith number of items 5, Capacity of the sack W=15, profit associated withthe items (p1,p2,…,p5)= (15,7,6,18,3) and weight associated with each item(w1,w2,…,w7)= (2,3,5,7,4, ).Consider the G-graph below. The numbers on the Edges are the gain values, not the cost. Now let's consider the Traveling Salesman Problem. The goal is to find the round that gives the maximum winnings (not the minimum cost). a) Apply the branch-and-bound algorithm to find the round with the maximum gain in the graph below. b) Is the branch-and-bound algorithm always guaranteed to find the optimal result? Is it a polynomial time algorithm?Please answer the following question in full detail. Please be specifix about everything: You have learned before that A∗ using graph search is optimal if h(n) is consistent. Does this optimality still hold if h(n) is admissible but inconsistent? Using the graph in Figure 1, let us now show that A∗ using graph search returns the non-optimal solution path (S,B,G) from start node S to goal node G with an admissible but inconsistent h(n). We assume that h(G) = 0. Give nonnegative integer values for h(A) and h(B) such that A∗ using graph search returns the non-optimal solution path (S,B,G) from S to G with an admissible but inconsistent h(n), and tie-breaking is not needed in A∗.
- For a double knapsack problem, assume follwoing 2 algorithms used. (1) Use the regular subset sum knapsack algorithm to pick a maximum-value solution S1 that fits in the first knapsack, and then use it again on the remaining items to pick a maximum-value solution S2 that fits in the second knapsack. (2) Use the Knapsack algorithm to pick a maximum-value solution S that would fit in a knapsack with capacity C1+C2, then partition S arbitrarily into two sets S1 and S2 with total sizes at most C1 and C2, respectively. Which of the following statements are true? (Choose all that apply.) a) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (2) is not. b) Algorithm (2) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (1) is not. c) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem when C1=C2. d) Neither algorithm is guaranteed to produce an…Consider a best first search (BFS) algorithm that tries to find the optimal goal state with minimal cost. Consider heuristics h1, h2 with h1(n) > h2(n) for all states n. BFS with h1 is guaranteed to expand fewer nodes or an equal number of nodes to arrive at the optimal goal state than BFS with h2 Select one: True FalseThe heuristic path algorithm is a best-first search in which the objective function is f(n)= 3w*g(n) + (2w+1) * h(n), 0≤w<3. For what values of w is this algorithm guaranteed to be optimal?