Before the advent of the simplex method for solving linear programming problems, the following method was used: Suppose you have a linear programming problem with two unknowns and 15 constraints. You locate corner points as follows: Selecting two of the constraints, you turn them into equations (by replacing the inequalities with equalities), solve the resulting system of two equations in two unknowns, and then check to see whether the solution is feasible. 1. How many systems of two equations in two unknowns will you be required to solve? 2. Generalize this to n constraints.
Before the advent of the simplex method for solving linear programming problems, the following method was used: Suppose you have a linear programming problem with two unknowns and 15 constraints. You locate corner points as follows: Selecting two of the constraints, you turn them into equations (by replacing the inequalities with equalities), solve the resulting system of two equations in two unknowns, and then check to see whether the solution is feasible.
1. How many systems of two equations in two unknowns will you be required to solve?
2. Generalize this to n constraints.
Given:
1) We have to find number of systems of two equations in two unknowns
We are given that there are 15 equations in two unknowns
2) We have to find number of systems of two equations in two unknowns chosen from n constraints.
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