SOLUTION: this time, our immune system is the best defense . With this, a Melegail wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 unit

Question 1178699: this time, our immune system is the best defense . With this, a Melegail wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food A contains 2 units /kg of Vitamin A and 1 unit of /kg of vitamin C. Food B contains 1 unit/kg of vitamin A and 2 units/kg of Vitamin C. It costs 50.00 per kg to purchase food A and 70.00 per kg to purchase Food B. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Absolutely! Let's formulate this as a linear programming problem.
**1. Define the Decision Variables:**
* Let `x` represent the number of kilograms of Food A.
* Let `y` represent the number of kilograms of Food B.
**2. Define the Objective Function:**
* The objective is to minimize the cost.
* Cost = 50x + 70y
* Minimize Z = 50x + 70y
**3. Define the Constraints:**
* **Vitamin A Constraint:** The mixture must contain at least 8 units of Vitamin A.
* 2x + y ≥ 8
* **Vitamin C Constraint:** The mixture must contain at least 10 units of Vitamin C.
* x + 2y ≥ 10
* **Non-negativity Constraints:** The amount of food cannot be negative.
* x ≥ 0
* y ≥ 0
**Complete Linear Programming Problem:**
**Minimize:** Z = 50x + 70y
**Subject to:**
* 2x + y ≥ 8
* x + 2y ≥ 10
* x ≥ 0
* y ≥ 0

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