(definition) Definition: The minimum (or maximum) value of the objective function over the feasible region of an optimization problem.
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What is optimal solution and optimal value?
An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.
What is optimal value of problem?
Optimal Value: In an optimization problem were the objective function is to be maximized the optimal value is the least upper bound of the objective function values over the entire feasible region.
How do you know if the optimal value is maximum or minimum?
Determine whether the function will have a minimum or a maximum depending on the coefficient of the x^2 term. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.
What is optimal value in linear programming?
If a linear programming problem can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.For example, the maximum or minimum value of f(x,y)=ax+by+c over the set of feasible solutions graphed occurs at point A,B,C,D,E or F .
What is an optimal solution in linear programming?
Definition: An optimal solution to a linear program is the feasible solution with the largest objective function value (for a maximization problem).
What do you mean by Modi method?
Abstract. The modified distribution method, is also known as MODI method or (u – v) method provides a minimum cost solution to the transportation problems.This model studies the minimization of the cost of transporting a commodity from a number of sources to several destinations.
What is optimal & feasible solution?
A feasible solution satisfies all the problem’s constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.
What is an optimum solution?
The term optimal solution refers to the best solution for a company to solve a problem or achieve its aims.An optimal solution uses resources most efficiently and effectively. It also yields the greatest possible return, considering the circumstances.
Is optimal value the same as vertex?
The optimal value is the highest or the lowest point on the parabola. The optimal value, also known as the vertex of the parabola would be maximum if only the parabola opens down words.
What is optimal solution in simplex method?
The optimal solution of a maximization linear programming model are the values assigned to the variables in the objective function to give the largest zeta value.
What is a maximum value?
The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph. If your quadratic equation has a negative a term, it will also have a maximum value.If you have the graph, or can draw the graph, the maximum is just the y value at the vertex of the graph.
How do you tell if a parabola is up or down?
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
How do you find the maximum and minimum of a set of data?
The maximum and minimum also make an appearance alongside the first, second, and third quartiles in the composition of values comprising the five number summary for a data set. The minimum is the first number listed as it is the lowest, and the maximum is the last number listed because it is the highest.
How do you find the optimal solution on a graph?
The largest or smallest value of the objective function is called the optimal value, and a pair of values of x and y that gives the optimal value constitutes an optimal solution. If an LP problem has optimal solutions, then at least one of these solutions occurs at a corner point of the feasible region.
What is an optimal basis?
A basis is locally optimal if its location x is the optimal solution to the linear program with the same objective function and only the constraints in the basis. Geometrically, a basis is locally optimal if its location x is the lowest point in the intersection of those d halfspaces.
What method is used to find optimal?
Usually, the initial basic feasible solution of any transportation problem is obtained by using well known methods such as North-West corner method (NWCM) or Least-Cost Method (LCM) or Vogel’s Approximation Method (VAM), and then finally the optimality of the given transportation problem is checked by MODI.
What is UV method?
What is U-V Method Optimality Test? U-V Method Optimality Test is used to check the optimality of a basic feasible solution consisting of (m+n-1) independent positive allocations and a set of arbitrary number ui and vj (i=1,2,…m; j=1,2,… n) such that cii= ui+vj for all occupied cells (i,j) .
Why Modi method is used?
The MODI (modified distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over other methods for solving transportation problems.
What is optimal solution in transportation problem?
Optimal Solution- a feasible solution is said to be optimal solution if it minimize total transportation cost Balanced Transportation Problem – a transportation problem in which the total supply from all sources is equal to the total demand in all the destinations.
What is primal and dual?
In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem.