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When solving linear prog. problems, we base our solutions on assumptions.one of these assumptions is that there is only one optimal solution to the problem.so in short NO. BY HADI
It is possible to have more than one optimal solution point in a linear programming model. This may occur when the objective function has the same slope as one its binding constraints.
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Can a linear programming problem have multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
How do you solve a fixed cost problem?
Fixed Cost Problem is a kind of the Mixed Linear Programming Problem(MILP).Also, MILP is a Parametric Quadratic Concave Programming Problem. The optimal solution is existence of vertix set of the domain set. Then, you can use the domain cutting method.
What do you understand by linear programming problem?
1. What do you understand by Linear Programming Problem? What are the requirements of Linear Programming Problem? What are the basic assumptions of Linear Programming Problem?
How do you find the answer to an integer problem?
It depends on the problem: you may have to use integer programming rather than linear programming.
Possible solutions to a problem which you could choose from?
possible solutions to a problem which you could choose from
Can a linear programming problem have two optimal solutions?
No. However, a special subset of such problems: integer programming, can have two optimal solutions.
Can a linear programming problem have exactly two optimal solutions?
Yes, a linear programming problem can have exactly two optimal solutions. This will be the case as long as only two decision variables are used within the problem.
What is the similar property between dynamic programming and greedy approach?
Both are using Optimal substructure , that is if an optimal solution to the problem contains optimal solutions to the sub-problems
Advantages of dynamic programming?
Dynamic programming enables you to develop sub solutions of a large program.the sub solutions are easier to maintain use and debug.And they possess overlapping also that means we can reuse them.these sub solutions are optimal solutions for the problem
What are the two properties that characterise a good dynamic programming problem?
Dynamic programming is a technique for solving problem and come up an algorithm. Dynamic programming divide the problem into subparts and then solve the subparts and use the solutions of the subparts to come to a solution.The main difference b/w dynamic programming and divide and conquer design technique is that the partial solutions are stored in dynamic programming but are not stored and used in divide and conquer technique.
How can one effectively implement dynamic programming in problem-solving techniques?
To effectively implement dynamic programming in problem-solving techniques, break down the problem into smaller subproblems, store the solutions to these subproblems in a table, and use these solutions to solve larger subproblems. This approach helps avoid redundant calculations and improves efficiency in finding optimal solutions.
Can a linear programming problem have multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
How can the coin change problem be solved using dynamic programming?
The coin change problem can be solved using dynamic programming by breaking it down into smaller subproblems and storing the solutions to these subproblems in a table. This allows for efficient computation of the optimal solution by building up from the solutions to simpler subproblems.
Advantages and disadvantages Dynamic programming?
Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems and solving each subproblem only once, storing the solutions in a table to avoid redundant calculations. The advantages of dynamic programming include efficient solution to complex problems, optimal substructure, and the ability to solve problems with overlapping subproblems. However, dynamic programming can be challenging to implement, requires careful problem decomposition, and may have high space complexity due to storing solutions in a table.
What is an optimization problem and how can it be effectively solved?
An optimization problem is a mathematical problem where the goal is to find the best solution from a set of possible solutions. It can be effectively solved by using mathematical techniques such as linear programming, dynamic programming, or heuristic algorithms. These methods help to systematically search for the optimal solution by considering various constraints and objectives.
How can the traveling salesman problem be efficiently solved using dynamic programming?
The traveling salesman problem can be efficiently solved using dynamic programming by breaking down the problem into smaller subproblems and storing the solutions to these subproblems in a table. This allows for the reuse of previously calculated solutions, reducing the overall computational complexity and improving efficiency in finding the optimal route for the salesman to visit all cities exactly once and return to the starting point.
What are the most effective strategies for solving the multiple knapsack problem efficiently?
One effective strategy for solving the multiple knapsack problem efficiently is using dynamic programming, which involves breaking down the problem into smaller subproblems and storing the solutions to these subproblems to avoid redundant calculations. Another strategy is using heuristics, such as the greedy algorithm, which makes decisions based on immediate benefit without considering the long-term consequences. Additionally, metaheuristic algorithms like genetic algorithms or simulated annealing can be used to find near-optimal solutions in a reasonable amount of time.
