# One kind of cake

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.

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