A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B. how many of each should be produced weekly in order to maximise the profit?

Explanation

To solve the problem of maximizing the profit for the toy company that manufactures two types of dolls, A and B, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( x \) = number of dolls of type A produced per week
- \( y \) = number of dolls of type B produced per week

### Step 2: Formulate the Constraints
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