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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.
What else can I help you with?
Can a linear programming problem have multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
Why does Phase 1 in linear programming have alternative optimal solutions?
Phase 1 of linear programming aims to find a feasible solution to the problem by minimizing a "penalty" function, often involving artificial variables. If the feasible region is unbounded or if multiple ways exist to achieve the same minimum value for the penalty function, there can be alternative optimal solutions. This occurs when the objective function is parallel to a constraint boundary, allowing for multiple feasible points that yield the same objective value. Hence, the presence of alternative optimal solutions is tied to the geometry of the feasible region and the nature of 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?
What do you understand by deneracy in transporation problem?
Degeneracy in a transportation problem occurs when there are more basic feasible solutions than necessary, typically when the number of occupied shipping routes (or allocations) is less than ( m + n - 1 ), where ( m ) is the number of supply points and ( n ) is the number of demand points. This situation can lead to multiple optimal solutions or cause difficulties in finding an optimal solution using methods like the Simplex algorithm. Degeneracy can also result in cycling during the optimization process, making it important to implement strategies to handle it effectively.
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
Can a linear programming problem have multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
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.
Why does Phase 1 in linear programming have alternative optimal solutions?
Phase 1 of linear programming aims to find a feasible solution to the problem by minimizing a "penalty" function, often involving artificial variables. If the feasible region is unbounded or if multiple ways exist to achieve the same minimum value for the penalty function, there can be alternative optimal solutions. This occurs when the objective function is parallel to a constraint boundary, allowing for multiple feasible points that yield the same objective value. Hence, the presence of alternative optimal solutions is tied to the geometry of the feasible region and the nature of the objective function.
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.
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.
What is the mean of optimal substructure?
Optimal substructure is a property of a problem that indicates it can be solved by combining the solutions of its subproblems. In other words, an optimal solution to a problem can be constructed from optimal solutions to its smaller, overlapping subproblems. This characteristic is essential in dynamic programming, where complex problems are broken down into simpler, manageable parts that can be solved independently and efficiently. Problems like the shortest path, knapsack, and Fibonacci sequence exhibit optimal substructure.
Advantages and disadvantages Dynamic programming?
...........................Advantages and Disadvantages of Dynamc Programming..................Dynamic programming provide a polynomial time solution.also used in that problem in which repetition may occur.Recall that the Dynamic Programming method is applicable when an optimal solution can be obtained from a sequence of decisions......................................................................................By Adnantufail islamia college peshawar.
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.
