Define a linear programming model and its components. Discuss which 3 properties a planning problem needs...

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Economics

Define a linear programming model and its components.Discuss which 3 properties a planning problem needs to meet to bemodeled as an LP?
Define the feasible set and its corner points. Explainhow one can find the combinations of the decision variablescorresponding to the corner points. How one can use the cornerpoints to find the optimal solution?
Define special situations: unbounded feasible set,infeasibility, alternate solutions, redundant constraints. Discusswhat do these situations imply for the manager's planning problem.When do you need to and how do you avoid thissituation?

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linear programming model leontiefs IO model can be interpreted as a simplified linear programming model Suppose that the final demand F1 and F2 are given The society likes to get thses final demands Now if X1 is the total output of the first industry then out of this a11x1 will be used up in the industry inself and a12X2 will be used up in the second industry The amount left is therefore X1 a11X1 a12X2 and it must be equal to the final consumption F1 if this final consumption is to be achieved From this relation we get one constraint 1a11X1 a12X2 F1 which will be utilised in the linear progamming formulation Similarly for the second industry we can get another constraint a21X1 1a22X2 F2 The gross output levels X1 and X2 cannot be negative so that X1 0 and X2 0 are the nonnegative conditions Consider now the objective function Here our problem is that the final demands F1 and F2 are specified To get these specified final demands we have to choose gross oupputs X1 and X2 in such a manner that the total labour cost is minimised The labour cost in money terms of X1 and X2 is equal to 11X1w12X2w This is the objective function to be minimised Thus in the Leontief model we get a typical linear programming problem which can be stated as follows Minimise W See Answer

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