CO227 Lecture 7: co 227 lec7

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Definition: given an lp, if we can assign values to the variables such that the constraints are satisfied, the values form a feasible solution of the lp. 3x1 + x2 <= 6 x1 + x2 >= 1 x1 = 1 is a feasible solution to the lp. (feasible lp) x2 = 2. Definition: if an lp has a feasible solution, then the lp is feasible. Max s. t. x1,x2 >= 0 x1 + x2. Definition: given an linear program with feasible solution x = ,the value of x is the value of the objective function using x. An optimal solution of an lp is a feasible solution that gives the best result for an lp. The value of the optimal solution is the optimal value. Max x1 + x2 s. t. x1+2x2 <= 10 x = is a feasible solution x has a value of 7 x*=is an optimal solution. x* has a value of 10.

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