(Diet problem): A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food II contains 1 unit/kg of vitamin A and 2 unite/kg of vitamin C. It costs Rs 50 per kg to purchase Food T and Rs 70 per kg to purchase Food II. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.

Explanation

To solve the diet problem as a linear programming problem, we need to follow a systematic approach. Here’s a step-by-step solution:

### Step 1: Define the Variables
Let:
- \( x \) = kg of Food I
- \( y \) = kg of Food II

### Step 2: Formulate the Objective Function
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