| 单词 | linear programming |
| 释义 | linear programming A mathematical procedure for finding the maximum or minimum value of a linear objective function subject to linear constraints. Where only small numbers of variables and constraints are involved, it is possible to proceed by assuming every possible set of the constraints to hold exactly and solving this as a system of simultaneous equations. Each solution is checked to see if the remaining constraints are satisfied: if they are it is feasible. The objective function can then be evaluated at every feasible solution and the feasible solution(s) giving the highest value for the objective function can be selected. If the number of variables concerned is large this procedure is impossible; linear programming works by selecting a set of constraints yielding one feasible solution, and adding constraints one by one, and excluding others, if making this change gives a feasible solution and increases the objective function; this procedure stops when no further change in the set of constraints can increase the objective function. The horizontal axis shows output of good X; the vertical axis shows output of good Y. The constraints are imposed by limits on the inputs available, where output of X and Y requires minimum quantities of each input per unit. ABC shows the constraint imposed by the available quantity of input 1; only outputs on or below ABC can be produced. DEBF shows the constraint imposed by the available quantity of input 2. GEH shows the constraint imposed by the available quantity of input 3. JK shows the constraint imposed by the available quantity of input 4. Input 4 will never be an effective constraint, but each of the others may be. The feasible set of outputs is shown by OGEBC. If production is at E, input 1 is not an effective constraint; if production is at B, input 3 is not an effective constraint. |
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