One kind of cake requires 300 gm of flour and 15 gm of fat, another kind of cake requires 150 gm of flour and 30 gm of fat. Find the maximum number of cakes which can be made from 7.5 kg of flour and 600 gm of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an LPP and solve it graphically.

Question

Philoid · Accepted Answer

The above information can be expressed in the form of the following table

Let ‘x’ and ‘y’ units of cake 1 and cake 2 be made.

Number of cakes made = x + y

Now,

⟹ 300x + 150y ≤ 7500

i.e. the maximum availability of flour is 7500g for both cakes, each of which requires 300g and 150g of flour respectively

⟹ 15x + 30y ≥ 600

i.e. the maximum availability of fat is 600g for both the cakes, each of which requires 15g and 30g of fat.

Hence , mathematical formulation of the LPP is as follows :

Find ‘x’ and ‘y’ that,

Maximises Z = x + y

Subject to the following constraints:

(i) 300x + 150y ≤ 7500

i.e. 2x + y ≤ 50

(ii) 15x + 30y ≥ 600

i.e. x + 2y ≥ 40

(iii) x,y ≥0 (∵ quantity cant be negative)

The feasible region is bounded (ABO)

The corner points of the feasible region is as follows:

Z is maximised at B(20,10)

The maximum number of cakes that can be made are 20 and 10 of each kind i.e. 30 in total.