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CBSE Class 12-science Answered

One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g 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 other ingredients, used in making cakes.
Asked by Topperlearning User | 01 Sep, 2014, 02:00: PM
answered-by-expert Expert Answer

Let x be the number of cakes of first kind and y of other kind, then we have following LPP
          Maximize x + y
          st 200x + 100y  5000 or 2x + y  50
          25x + 50y  1000 or x + 2y  40
          x,y  0
         

Corner Points

z = x + y

A(25, 0)
B(20, 10)
C(0, 20)

z = 25
z = 30
z = 20

Since the highest number of cakes in the second column of the above table is Z=30, the maximum occurs at B(20,10)

Thus, the number of first kind of cake is 20 and the number of second kind of cake is 10.

Answered by | 01 Sep, 2014, 04:00: PM

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