Question

One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.

Answer 1

Z = x + y subject to the constraints 

(i) 200 x + 100y ≤ 5000 ⇒ 2x + y <50 

(ii) 25x + 50y ≤ 1000 ⇒ x + 2y < 40 

(iii) x , y ≥ 0

A (0, 0 ) Z = 0 

B (25, 0) Z = 25 + 0 = 25 

C(20, 10) Z = 20+10 = 30 

D (0, 20) Z = 0 + 20 = 20 

At C (20, 10) maximum number of cakes can be made.