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What is the difference between feasible solution and basic feasible solution?
optimal solution is the possible solution that we able to do something and feasible solution is the solution in which we can achieve best way of the solution
What is primal simplex method?
II. SIMPLEX ALGORITHM A. Primal Simplex Algorithm If the unconstrained solution space is defined in n dimensions (each dimension assumed to be infinite), each inequality constraint in the linear programming formulation divides the solution space into two halves. The convex shape defined in n-dimensional space after m bisections represents the feasible area for the problem, and all points which lie inside this space are feasible solutions to the problem. Figure 1 shows the feasible region for a problem defined in two variables, n = 2, and three constraints, m = 3. Note that in linear programming, there is an implicit non-negativity constraints for the variables. The linearity of the objective function implies that the the optimal solution cannot lie within the interior of the feasible region and must lie at the intersection of at least n constraint boundaries. These intersections are known as corner- point feasible (CPF) solutions. In any linear programming problem with n decision variables, two CPF solutions are said to be adjacent if they share n − 1 common constraint boundaries. When interpreted geometrically, the Simplex algorithm moves from one corner-point feasible solution to a better corner-point-feasible solution along one of the constraint boundaries. There are only a finite number of CPF solutions, although this number is potentially exponential in n, however it is not necessary to visit all of them to determine the optimal solution to the problem. The convex nature of linear programming means that there are no local maxima present in the problem which are not also global maxima. Hence if at some CPF solution, no improvement is made by a move to another adjacent CPF then the algorithm terminates and we can be confident that the optimal solution has been found.
What is dynamic routing?
Routing refers to the process of moving packets of information across a network. Static and dynamic routing are the two types of routing algorithms used for this transfer of information.The term routing encapsulates two tasks. These tasks are deciding the paths for data transferred and sending the packets on these paths. The routing is a process that is a function carried out at layer 3 of the OSI reference model. The routing algorithm decides the output line to transfer the incoming packets. The routing algorithms are based on the routing protocol that uses metrics to assess whether a particular path is the optimal path available for transfer of the data packets. The metrics used for evaluating the paths are bandwidth, delay and reliability. The routing algorithms use these protocols to determine an optimal path from the source to the destination. The routing tables maintain all the information related to routing. There are various routing algorithms and depending on these routing algorithms, the information stored in the routing table varies. Every router has its own routing table and it fills this table with the required information to calculate the optimal path between the source router and the destination router. To understand the basic points of static vs dynamic routing, let us get to know what are routing tables.Routing tableA routing table is a document stored in the router or a network computer. The routing table is stored in the form of a database or is simply a file stored in the router. The data entered in the routing table is referred to when the best possible path to transfer information across two computers in a network is to be determined. The two classifications, viz., static and dynamic routing, are based on the way in which the routing tables are updated every time they are used. The routers in which the data is stored and updated manually are called static routers. On the other hand, the routers in which the information is changed dynamically, by the router itself, are referred to as dynamic routers. Let us compare the two types of routing algorithms based on the static and dynamic routing algorithm used, in the static vs. dynamic routing section given below.Static Vs. Dynamic RoutingStatic routing manually sets up the optimal paths between the source and the destination computers. On the other hand, the dynamic routing uses dynamic protocols to update the routing table and to find the optimal path between the source and the destination computers.The routers that use the static routing algorithm do not have any controlling mechanism if any faults in the routing paths. These routers do not sense the faulty computers encountered while finding the path between two computers or routers in a network. The dynamic routing algorithms are used in the dynamic routers and these routers can sense a faulty router in the network. Also, the dynamic router eliminates the faulty router and finds out another possible optimal path from the source to the destination. If any router is down or faulty due to certain reasons, this fault is circulated in the entire network. Due to this quality of the dynamic routers, they are also called adaptive routers.The static routing is suitable for very small networks and they cannot be used in large networks. As against this, dynamic routing is used for larger networks. The manual routing has no specific routing algorithm. The dynamic routers are based on various routing algorithms like OSPF (Open Shortest Path First), IGRP (Interior Gateway Routing Protocol) and RIP (Routing Information Protocol).The static routing is the simplest way of routing the data packets from a source to a destination in a network. The dynamic routing uses complex algorithms for routing the data packets.The static routing has the advantage that it requires minimal memory. Dynamic router, however, have quite a few memory overheads, depending on the routing algorithms used.The network administrator finds out the optimal path and makes the changes in the routing table in the case of static routing. In the dynamic routing algorithm, the algorithm and the protocol is responsible for routing the packets and making the changes accordingly in the routing table.Nowadays, the static routing is seldom used. With the technological advancements, the dynamic routing is used to route the packets in the network, efficiently. Thus, the above algorithm explains routing, routing tables and static vs dynamic routing.
How much do 9000 BTU cover?
A 9,000 BTU air conditioner can effectively cool a room of approximately 300 to 400 square feet, depending on factors such as ceiling height, insulation, and sun exposure. It's suitable for small to medium-sized rooms, like bedrooms or home offices. For optimal performance, ensure the unit is correctly sized for the specific conditions of the space.
How many square feet does an 48000 but air conditioner cool?
An air conditioner with a cooling capacity of 48,000 BTUs typically cools an area of approximately 2,000 to 3,000 square feet, depending on various factors such as ceiling height, insulation quality, and climate. It's important to consider these factors for optimal performance. For accurate cooling capacity, consulting the manufacturer's specifications and guidelines is advisable.
What is the difference between feasible and optimal solution?
The optimal solution is the best feasible solution
What is the difference between feasible solution and basic feasible solution?
optimal solution is the possible solution that we able to do something and feasible solution is the solution in which we can achieve best way of the solution
Why optimal solution is only at corner point?
feasible region gives a solution but not necessarily optimal . All the values more/better than optimal will lie beyond the feasible .So, there is a good chance that the optimal value will be on a corner point
What is optimal solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
What is the difference between greedy algorithm and Divide and Conquer?
greedy method does not give best solution always.but divide and conquer gives the best optimal solution only(for example:quick sort is the best sort).greedy method gives feasible solutions,they need not be optimal at all.divide and conquer and dynamic programming are techniques.
What is optimal feasible solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
Is (-12) a one solution?
A solution is Pareto optimal if there exists no feasible solution for which an improvement in one objective does not lead to a simultaneous degradation in one (or more) of the other objectives. That solution is a nondominated solution.
Non-degenerate basic feasible solution?
A non-degenerate basic feasible solution in linear programming is one where at least one of the basic variables is strictly positive. In contrast to degenerate solutions where basic variables might be zero, non-degenerate solutions can help optimize algorithms as they ensure progress in the search for the optimal solution.
What is the strong duality proof for linear programming problems?
The strong duality proof for linear programming problems states that if a linear programming problem has a feasible solution, then its dual problem also has a feasible solution, and the optimal values of both problems are equal. This proof helps to show the relationship between the primal and dual problems in linear programming.
Is it possible for an linear programming model to have exact two optimal solutions?
Yes, but only if the solution must be integral. There is a segment of a straight line joining the two optimal solutions. Since the two solutions are in the feasible region part of that line must lie inside the convex simplex. Therefore any solution on the straight line joining the two optimal solutions would also be an optimal solution.
Is Feasible region is necessary to be a convex set?
Yes, in optimization problems, the feasible region must be a convex set to ensure that the objective function has a unique optimal solution. This is because convex sets have certain properties that guarantee the existence of a single optimum within the feasible region.
What is the difference between simplex and dual simplex problem?
The simplex method is an algorithm used to solve linear programming problems, typically starting from a feasible solution and moving toward optimality by improving the objective function. In contrast, the dual simplex method begins with a feasible solution to the dual problem and iteratively adjusts the primal solution to maintain feasibility while improving the objective. The dual simplex is particularly useful when the primal solution is altered due to changes in constraints, allowing for efficient updates without reverting to a complete re-solution. Both methods ultimately aim to find the optimal solution but operate from different starting points and conditions.
