Linear Programming Problem: Minimizing Cost of Food with Vitamin Requirements **Decision Variables:** Let x1, x2, and x3 be the units of foods F1, F2, and F3 respectively. **Objective Function:** Minimize Z = 20x1 + 24x2 + 18x3 **Constraints:**

Linear Programming Problem: Minimizing Cost of Food with Vitamin Requirements

Decision Variables: Let $x_1$, $x_2$, and $x_3$ be the units of foods $F_1$, $F_2$, and $F_3$ respectively.

Objective Function: Minimize $Z = 20x_1 + 24x_2 + 18x_3$

Constraints: $$20x_1 + 10x_2 + 10x_3 \geq 300 \quad \text{(Vitamin } V_1 \text{ requirement)}$$ $$10x_1 + 10x_2 + 10x_3 \geq 200 \quad \text{(Vitamin } V_2 \text{ requirement)}$$ $$10x_1 + 20x_2 + 10x_3 \geq 240 \quad \text{(Vitamin } V_3 \text{ requirement)}$$ $$x_1, x_2, x_3 \geq 0 \quad \text{(Non-negativity constraints)}$$