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A diet is to contain not more than 4000 units of carbohydrates, at least 500 units of fat and 300 units of protein. Two foods Combo 1 and Combo 2 are available. Combo 1 costs P600 per unit and Combo 2 costs P300 per unit. A unit of Combo 1 contains not more than 10 units of carbohydrates while Combo 2 contains 25 units of the same. Additionally, Combo 1 contains at least 20 units of fat and 15 units of protein. And Combo 2 contains 10 units of fat and 20 units of protein minimum requirement.

Find the minimum cost for a diet that consists of a mixture of these two foods.
Show steps by steps

1. what is the objective funtion
2. how many constraints does the problem have?
3. how many corner points are there in the feasible region?
4. what is the value of Y at Point B?
5. what is the value of X at Point C?
6. what amount of cost at Point B?
7. how much is the minimum cost of the optimal solution?​

Sagot :

johnreystarosa46

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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