One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100 g 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.

Explanation

To solve the problem of maximizing the number of cakes that can be made from the available flour and fat, we will follow these steps:

### Step 1: Define Variables
Let:
- \( X \) = number of the first kind of cake
- \( Y \) = number of the second kind of cake

### Step 2: Set Up Constraints
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