SOLUTION: ABC Dairy Company wishes to make a new cheese from two of its current cheeses: Cheese X and Cheese Y. The mixture is to weight at least than 4 pounds and is to contain 6 ounces of

Question 1199840: ABC Dairy Company wishes to make a new cheese from two of its current cheeses: Cheese X and Cheese Y. The mixture is to weight at least than 4 pounds and is to contain 6 ounces of the sharpness Ingredients S. Each pound of X costs $4 and contains 3 ounces of S, whereas each pound of Y costs $1 and contains one ounce of S. find the minimum cost of the mixture if the amount of Cheese Y cannot exceed the amount of Cheese X by more than one pound.
Answer by ElectricPavlov(122) (Show Source): You can put this solution on YOUR website!
**1. Define Variables**
* Let 'x' be the amount of Cheese X in pounds.
* Let 'y' be the amount of Cheese Y in pounds.
**2. Formulate Constraints**
* **Weight Constraint:** x + y ≥ 4 (Total weight must be at least 4 pounds)
* **Sharpness Ingredient Constraint:** 3x + y ≥ 6 (Total amount of ingredient S must be at least 6 ounces)
* **Constraint on Cheese Y:** y - x ≤ 1
**3. Define Objective Function**
* **Cost Function (to be minimized):**
* Cost = 4x + 1y
**4. Graphical Representation**
* **Plot the constraints:**
* x + y ≥ 4
* 3x + y ≥ 6
* y - x ≤ 1
* **Find the feasible region:**
* The feasible region is the area on the graph that satisfies all the constraints simultaneously.
* **Identify the corner points of the feasible region.**
**5. Evaluate the Objective Function at Corner Points**
* Calculate the cost at each corner point of the feasible region.
**6. Determine the Minimum Cost**
* The corner point with the lowest cost value provides the minimum cost of the mixture.
**Note:**
* This problem can be solved graphically by plotting the constraints and finding the feasible region.
* Alternatively, you can use linear programming techniques (such as the simplex method) to find the optimal solution.
**To find the exact solution, you would need to:**
1. **Graph the constraints**
2. **Identify the feasible region**
3. **Determine the corner points**
4. **Calculate the cost at each corner point**
The corner point with the lowest cost will give you the minimum cost of the mixture and the optimal amounts of Cheese X and Cheese Y.

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