1. **Problem Statement:** A dietician wants to mix two foods to get at least 8 units of vitamin A and 10 units of vitamin C in the mixture. Food I has 2 units/kg vitamin A and 1 unit/kg vitamin C, costing 50 per kg. Food II has 1 unit/kg vitamin A and 2 units/kg vitamin C, costing 70 per kg. The goal is to minimize the cost. 2. **Define Variables:** Let $x$ = kg of Food I Let $y$ = kg of Food II 3. **Formulate Constraints:** Vitamin A requirement: $$2x + y \geq 8$$ Vitamin C requirement: $$x + 2y \geq 10$$ Non-negativity: $$x \geq 0, y \geq 0$$ 4. **Objective Function:** Minimize cost: $$Z = 50x + 70y$$ 5. **Linear Programming Model:** \[ \text{Minimize } Z = 50x + 70y \] subject to \[ 2x + y \geq 8 \] \[ x + 2y \geq 10 \] \[ x \geq 0, y \geq 0 \] This is the required linear programming formulation to minimize the cost while meeting vitamin requirements.