Question

One kind of cake requires 200 g of flour and 25 g of fat, 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 it an LPP and solve it graphically

Answer 1

Let the company make x no of 1^st kind and y no of 2^nd cakes.

∴According to the question,

200x + 100y ≤ 5000, 25x + 50y ≤ 1000, x ≥ 0, y ≥ 0

Maximize Z = x + y

The feasible region determined by 200x + 100y ≤ 5000, 25x + 50y ≤ 1000, x ≥ 0, y ≥ 0 is given by

The corner points of feasible region are A(0,0) , B(0,20) , C(20,10) , D(25,0).

The value of Z at corner point is

Corner Point	Z = x + y
A(0, 0)	0
B(0, 20)	20
C(20, 10)	30	Maximum
D(25, 0)	25

The maximum value of Z is 30 and occurs at point (20,10).

The company should make 20 of 1^st type and 10 of 2^nd type.