A Certain Linear Programming Problem Has Four Functional Constraints in Inequality

question 2

Essay

A certain linear programming problem has four functional constraints in inequality form such that their right-hand sides (the b_i)are uncertain parameters.Therefore,chance constraints with $\alpha$ = 0.95 have been introduced in place of these constraints.After next substituting the deterministic equivalents of these chance constraints and solving the resulting new linear programming model,its optimal solution is found to satisfy two of these deterministic equivalents with equality whereas there is some slack in the other two deterministic equivalents.Determine the lower bound and the upper bound on the probability that all of these four original constraints will turn out to be satisfied by the optimal solution for the new linear programming model so this solution actually will be feasible for the original problem.

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