Question

One kind of cake requires 300 g of flour and 15 g of fat, another kind of cake requires 150 g of flour and 30 g of fat. Find the maximum number of cakes which can be made from 7 × 5 kg of flour and 600 g of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it as an L.P.P. and solve it graphically.

Answer 1

Let number of first kind and second kind of cakes that can be made be x and y respectively 

Then, the given problem is 

Maximize, z = x + y

Subjected to x ≥ 0, y ≥ 0 

300x + 150y ≤ 7500 ⇒ 2x + y ≤ 50 

15x + 30y ≤ 600 

⇒ x + 2y ≤ 40 

On plotting graph of above constraints or inequalities, we get shaded region. 

From graph, three possible points are (25, 0), (20, 10), (0, 20) 

At (25, 0), z = x + y = 25 + 0 = 25 

At (20, 10), z = x + y = 20 + 10 = 30 ← Maximum 

At (0, 20), z = 0 + 20 = 20 

As Z is maximum at (20, 10), i.e., x = 20, y = 10. 

∴ 20 cakes of type I and 10 cakes of type II can be made.