In a two-class, two-action problem, if the loss function is A11 A12 = 10, and A21 = 1, write the optimal decision rule. = A22 = 0,
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- Solve the following optimization problems using Gurobi and clearly present the optimal objective function value and decision variable values at optimality. (Java Programming) maximize 3x + 4y − 2z + 10 subject to 2x + 3y − z ≤ 50 x + y + 3z ≥ 30 x unrestricted, y ≥ 0, z ≥ 0, and integerA two-person zero-sum game is given by the matrix A := −2 −3 2 −1, 2 1 −5 2, 0 −4 4 −3, 1 −2 3 0 . Find a pair of optimal strategies for this game as well as the value of the game.If it is possible to create an optimal solution for a problem by constructing optimal solutions for its subproblems, then the problem possesses the corresponding property. a) Subproblems which overlap b) Optimal substructure c) Memorization d) Greedy
- If it is possible to construct an optimal solution for a problem by constructing optimal solutions for its subproblems, then the problem possesses the specified property. a) Overlapping subproblems; b) optimal substructure; c) memorization; d) greedySuppose X and Y are decision problems for which X≤PY, i.e., X is polynomial-time reducible to Y . If X is NP-complete and Y is in NP, explain why Y must also be NP-complete.Any linear program L, given in standard form, either1. has an optimal solution with a finite objective value,2. is infeasible, or3. is unbounded.If L is infeasible, SIMPLEX returns “infeasible.” If L is unbounded, SIMPLEXreturns “unbounded.” Otherwise, SIMPLEX returns an optimal solution with a finiteobjective value.
- Calculate the optimal value of the decision parameter p in the Bresenham's circle drawing algorithm. The stepwise procedure for implementing Bresenham's algorithm for circle drawing is delineated.Insufficient Overlapping Subproblems and the Principle of Optimality (Optimal Substructure) are dynamic programming questions. As an example, consider All-Pairs Shortest Paths.The 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?
- Using the image provided, please answer the following questions. (a). Find a path from a to g in the graph G using the search strategy of depth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (b). Find a path from a to g in the graph G using the search strategy of breadth-first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal".(c). Find a path from a to g in the graph G using the search strategy of least-cost first search. Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal" or "why-non-optimal". (d). Find a path from a to g in the graph G using the search strategy of best-first search. The heuristics for these nodes are: h(a,25); h(b, 43); h(c,5); h(d, 64); h(g, 0). Is the returned solution path an optimal one? Give your explanation and remarks on "why-optimal or "why-non-optimal".…If the optimal solution of a linear programming problem with two constraints is x=5, y=0, s1=3 and s2=0 , then the basic variables are ____.Constructing an Optimal Solution:algorithm LCSWithAdvice x1, ... , xi, y1, ... , yj, birdAdvice pre- & post-cond: Same as LCS except with advice.