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LINEAR PROGRAMMING

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Optimisation Problem A problem which seeks to maximise or minimise afunction is called an optimisation problem. An optimisation problem mayinvolve maximisation of profit, production etc or minimisation of cost, from availableresources Linnear PROGRAMMING Problem (LPP)A LINEAR PROGRAMMING problem deals with the optimisation (maximisation/minimisation) of alinear function of two variables (sayx andy) known asobjectivefunctionsubject to the conditions that the variables are non-negative and satisfy a setof LINEAR inequalities (calledlinear constraints). A LINEAR PROGRAMMING problem is aspecial type of optimisation Function LINEAR function Z =ax+by, wherea and b are constants,which has to be maximised or minimised is called a LINEAR objective VariablesIn the objective function Z =ax +by,x andy are calleddecision The LINEAR inequalities or restrictions on the variables of an LPPare calledconstraints.

State whether the statements in Examples 11 and 12 are True or False. Example 11 If the feasible region for a linear programming problem is bounded, then the objective function Z = ax + by has both a maximum and a minimum value on R.

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