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m →Overview: and <math> \mathbf{x} = (x_1,\, \dots,\, x_n)</math> the variables of the problem → and <math> \mathbf{x} = (x_1,\, \dots,\, x_n)</math> are the variables of the problem {the singular "is" in the previous clause does not carry over to the current clause with a plural subject} |
→Overview: {added another "are" where "is" in previous clause does not carry over; removed spurious "."} |
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:subject to <math>A\mathbf{x} \leq \mathbf{b}</math> and <math>\mathbf{x} \ge 0</math>
with <math>\mathbf{c} = (c_1,\, \dots,\, c_n)</math> the coefficients of the objective function, <math>(\cdot)^\mathrm{T}</math> is the [[matrix transpose]], and <math> \mathbf{x} = (x_1,\, \dots,\, x_n)</math> are the variables of the problem, <math>A</math> is a ''p×n'' matrix, and <math> \mathbf{b} = (b_1,\, \dots,\, b_p)</math> are nonnegative constants (<math>\forall j, b_j \geq 0\ </math>)
In geometric terms, the [[feasible region]] defined by all values of <math>\mathbf{x}</math> such that <math display="inline">A\mathbf{x} \le \mathbf{b}</math> and <math>\forall i, x_i \ge 0 </math> is a (possibly unbounded) [[convex polytope]]. An extreme point or vertex of this polytope is known as ''[[basic feasible solution]]'' (BFS).
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