operations research optimal solution minimization maximization double integral solved exercises antiderivatives network analysis parametric representation integral over closed curve exact differential form line integral green riemann theorem rules in constructing a network predecessors and successors activities concurrent activities dummy activity constructing a network artificial variable surplus variable big m method simplex method graphical method linear programming steps in solving operations research problems characteristics of operations research partial derivatives of a function of two variables limits for functions of two variables function of several variables polar coordiantes general region rectangular region simple integration simple integral critical path cpm transportation stepping stone method vogel approximation method least cost entry method north west corner method sensitivity analysis
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