linear programming problem in a sentence

Examples

1. A linear programming problem is one in which we wish to maximize or minimize a linear objective function of real variables over a polytope.
2. According to George Dantzig, the duality theorem for linear optimization was conjectured by John von Neumann immediately after Dantzig presented the linear programming problem.
3. The mathematical linear programming problem is defined on the real numbers, and even storing a real number on a computer is impossible in general.
4. This algorithm which is almost like obtaining a solution of linear equations has been found to be extremely useful in solving most linear programming problems.
5. Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and for his other work with linear programming.
6. The combinatorial problems above are, in fact, mixed 0 1 linear programming problems that can be solved by using branch-and-bound algorithms.
7. The method proceeds by first dropping the requirement that the x i be integers and solving the associated linear programming problem to obtain a basic feasible solution.
8. For example, the simplex method for the solution of linear programming problems was worked out and widely applied prior to the development of much of programming theory.
9. :Note : the original formulation of this problem, requirement that the combined land mass be contiguous, is a simple 0-1 linear programming problem.
10. In fact, for some time it was not known whether the linear programming problem was solvable in polynomial time, i . e . of complexity class P.