Question

One kind of cake required 300g of flour and 15g of fat, another kind requires 150gm of flour and 30gm of fat. Find the maximum number of cakes which can be made from 7.5kg of flour and 600gm of fat.

Answer 1

Let the 1st type of cake x and 2nd type of cake be y 

∴ maximize z = x + y subject to 

300x + 150 y ≤ 7500, 2x + y ≤ 50 

15x + 30y ≤ 600

x + 2y ≤ 40 

x ≤ 0, y ≤ 0

comer point are (0,0), (25,0) (20, 10), (0, 20) 

At 0, Z = 0 

A, Z = 25 

B, Z = 30 – Maximum 

C, C = 20 

Maximum at B (20, 10) 

∴ 20 pieces of 1 st type and 10 pieces of 2nd type cake