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In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for maximization problem, decrease for minimization problem) before it would be possible for a corresponding variable to assume a positive value in the optimal solution.
The cost-minimization problem of the firm is to choose an input bundle (K,L) feasible for the output level y that costs as little as possible. A cost-minimizing input bundle is a point on the isoquant for the given y that is on the lowest possible isocost line. Put differently, a cost-minimizing input bundle must satisfy two conditions:
In microeconomics, the utility maximization problem and its dual problem, the expenditure minimization problem, are economic optimization problems. Insofar as they behave consistently, consumers are assumed to maximize their utility , while firms are usually assumed to maximize their profit .
In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: "how much money do I need to reach a certain level of happiness?". This question comes in two parts. Given a consumer's utility function, prices, and a utility target,
After the problem on variables +, …, is solved, its optimal cost can be used as an upper bound while solving the other problems, In particular, the cost estimate of a solution having x i + 1 , … , x n {\displaystyle x_{i+1},\ldots ,x_{n}} as unassigned variables is added to the cost that derives from the evaluated variables.
If m = p = 0, the problem is an unconstrained optimization problem. By convention, the standard form defines a minimization problem . A maximization problem can be treated by negating the objective function.
Isocost v. Isoquant Graph. In the simplest mathematical formulation of this problem, two inputs are used (often labor and capital), and the optimization problem seeks to minimize the total cost (amount spent on factors of production, say labor and physical capital) subject to achieving a given level of output, as illustrated in the graph.
The quickest path problem is a cost-minimization problem. [3] The goal is to send a message between two points in a communication network, which is modeled as a graph. Each computer in the network is modeled as an edge in the graph.