Question

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. Formulate the above as an LPP and solve it graphically

Answer 1

Let x be the number of cakes of one kind and y be the number of cakes of other kind.

To maximize: Z = (x + y)

Subject to constraints:

Corner Points	Value of Z
O(0, 0)	0
A(0, 20)	20
B(20, 10)	30
C(25, 0)	25

Clearly, maximum value of Z is 30.

Hence the no. of cake of one kind = 20, and, the no. of cake of another kind = 10.