Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60 / kg and Food Q costs Rs 80 / kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

Explanation

To solve the problem step-by-step, we will follow the linear programming approach to minimize the cost of mixing two types of food, P and Q, while satisfying the vitamin requirements.

### Step 1: Define Variables
Let:
- \( x \) = kg of food P
- \( y \) = kg of food Q

### Step 2: Formulate the Objective Function
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