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One kind of cake requires 200 g of fl...

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 the other ingredients used in making the cakes. Make an L.P.P. of the above and solve it graphically.

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Let `x` cakes of first type and `y` cakes of second type be made.

According to the problem maximise `Z=x+y`, and constraints `xge0`
`yge0`
`200x+100yle5000implies2x+yle50`
`25x+50yle1000impliesx+2yle40`
First draw the graph of the straight lines `2x+y=50` and `x+2y=40`.

Now find the feasible region using constraints `2x+yle50, x+2yle40, xge0,yge0` and shade it. The vertices of this shaded region are `A(25,0),B(20,10)` and `C(0,20)`. We find the value of `Z` at these vertices.

Therefore 20 cakes of first types and 10 cakes fo second types are made.
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