Answer:
To solve this linear programming problem step by step:
Given Data:
- Combo 1 Cost: P600 per unit
- Combo 2 Cost: P300 per unit
- Nutritional Constraints: Carbohydrates, Fat, and Protein requirements for the diet
1. Objective Function:
The objective is to minimize the cost of the diet. Let:
- X: Number of units of Combo 1
- Y: Number of units of Combo 2
The objective function is:
Z = 600X + 300Y
2. Constraints:
The problem has the following constraints:
1. Carbohydrates constraint: 10X + 25Y \leq 4000
2. Fat constraint: 20X + 10Y \geq 500
3. Protein constraint: 15X + 20Y \geq 300
4. Non-negativity constraints: X, Y \geq 0
3. Feasible Region:
To find the feasible region, graph the inequalities and identify the corner points where the constraints intersect.
4. Value of Y at Point B:
At Point B, one of the constraints will be binding. Calculate the intersection of the relevant constraints to find the value of Y at Point B.
5. Value of X at Point C:
Similarly, calculate the intersection of relevant constraints to find the value of X at Point C.
6. Cost at Point B:
Substitute the values of X and Y at Point B into the objective function to find the cost at Point B.
7. Minimum Cost of the Optimal Solution:
After determining the cost at each corner point, identify the corner point with the minimum cost. This will give you the optimal solution for the minimum cost diet.
By following these steps and solving the linear programming problem using the given data and constraints, you can determine the minimum cost for a diet that consists of a mixture of Combo 1 and Combo 2 foods.
Step-by-step explanation:
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