12th Class Mathematics Linear Programming

  • question_answer 27) Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F, whose requirements are 60, 50 and 40 quintals respectively.       The cost of transportation per quintal from the godowns to the shops are given in the following table :             How should the supplies the transported in order that the transportation cost is minimum cost ?  

    Answer:

    Let Depot A transport x litres of petrol to petrol pump D, y litres to e and 7000 ? (x + y) litres to C.       Also, let depot B transport (4500-x) lietres of petrol to petrol pump to D, (3,000-y) litres to E and x + y ? 3500 to F.       Graphical representation of the problem is given below :       Here objective function is       C = 7x + 6y + 3 (700 ? x ? y) + 3 (4500 ? x) + 4 (3000 ? y) + 2(x + y ? 3500)       i.e. C = 3x + y + 39500 subject to the constraints x + y  x + y ?3500        i.e. Minimize, C = 3x + y + 39,500 subject to the constraints x + y             L1 : x + y = 7000                  L2 : x + y = 3500                   Here cost is minimum at H(500, 3000)       Hence from depot A, 500/, 3000/, 3500/ petrol will be transported to petrol pumps D, e,f F respectively and from Dept B, 4000/, ol, ol petrol will be transported to petrol pumps D, E, F respectively.       Since transportation cost of 10/is Rs.1 per km        Total transportation cost  

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