12th Class Mathematics Linear Programming

  • question_answer 12) One kind of cake requires 200 g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients, used in making the cakes. 

    Answer:

    Let number of cakes of first kind = x       and the number of cakes of second kind = y       The contents of cake are given below

    Cake Flour Fat
    First kind 200 25
    Second Kind 100 50
    Quantity available 5 kg 1 kg
          Therefore the above L.P.P. is given as maximize,       Z = x + y, subject to the constraints.             200 x + 100 y       and 25x + 50 y       i..e.             2x + y       and x + 2y       L1: 2x + y = 50                     L2 : x + 2y = 40                                               Here Z is maximum at E(20, 10)        Number of cake of first kind x =20       Number of cakes of second kind, y = 10        Maximum number of cakes = 20 +10 = 30.    

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