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A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
1. At the tangent point, i.e. Portfolio P, is the optimum combination of risky investments and the market portfolio. 2. Only efficient portfolios that consist of risk free investments and the market portfolio P lie on the CML. 3. CML is always upward sloping as the price of risk has to be positive.
2. The strong duality theorem provides a "good characterization" of the optimal value of an LP in that it allows us to easily prove that some value t is the optimum of some LP. The proof proceeds in two steps: [4]: 260–261 Show a feasible solution to the primal LP with value t; this proves that the optimum is at least t.
The strong duality theorem states that if the primal has an optimal solution, x *, then the dual also has an optimal solution, y *, and c T x * =b T y *. A linear program can also be unbounded or infeasible. Duality theory tells us that if the primal is unbounded then the dual is infeasible by the weak duality theorem.
Optimum suit combination play allows for all possible lies of the cards held by the defenders. The term is also used for the sequence of plays [ 2 ] from the declarer and dummy hands, conditional on intervening plays by the opponents; in other words, declarer's plan or strategy of play given his holdings and his goal for the number of tricks to ...
High-quality statistical software provide a combination of libraries of optimal designs or iterative methods for constructing approximately optimal designs, depending on the model specified and the optimality criterion. Users may use a standard optimality-criterion or may program a custom-made criterion.
An isocost line is a curve which shows various combinations of inputs that cost the same total amount . For the two production inputs labour and capital, with fixed unit costs of the inputs, the isocost curve is a straight line . The isocost line is always used to determine the optimal production combined with the isoquant line .
In economics and microeconomics, the economic region of production is an offshoot of the theory of production function with two variables. It is a cost-oriented theory which defines the region in which the optimal factor combination will lie. [1]
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