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.

Explanation

let one lind of cake = x

other kind of cake = y

according to question

`x>= 0 & y>=0` eqn(1) & (2)

`200x + 100y <= 5000`

`2x + y <=50` eqn(3)

also, `25x + 50y <= 1000`

`x+2y <= 400` eqn(4)

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