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...Linear programming introduction was developed in by george b dantzig marshal wood and their associates it deals with the optimization maximization or minimization of a function variables known as objective functions is set equalities inequalities constraint basically mathematical technique which involves allocations limited resources an optimal manner on basis given criterion optimality method applicable for solution problems constraints appear decision basic definitions these are whose quantitative values to be found from model so maximize minimize usually denoted x xn may controllable uncontrollable those under control makers not determinants quantity either maximized minimized must include all possibilities profit cost coefficient per unit output z can stated max min c n restrictions imposed terms availability raw materials machine hours man etc ai ain bi m mn equation represents role constants non negative also s ij j above l p expressed form matrix follows opt cx subject ax where ...