One kind of cake requires 300 gm of flour and 15 gm of fat and another kind of cake requires 150 gm of flour and 30 gm of fat. Find the maximum number of cakes that can be made from 7.5 kg of flour and 600 gm of fat. Form a linear programming problem and solve it graphically.

One kind of cake requires 100 gm of flour and 50 gm of fat and another kind of cake requires 50 gm of flour and 100 gm of fat. Find the maximum number of cakes that can be made from 4 kg of flour and 5 kg of fat. Form a linear programming problem and solve it graphically.

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.