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Answer :
Final answer:
To minimize costs while meeting protein and fat requirements for dog food production at Ruff, Inc., we need to solve a Linear Programming problem. This involves minimizing a cost function subject to constraints on protein and fat content. The answer will determine the optimal ounces of chicken and grain to use per bag of dog food.
Explanation:
The question is about using the minimum amount of chicken and grain in dog food production at Ruff, Inc. to meet or exceed the required protein and fat content at the lowest cost. To solve this, we need to formulate a Linear Programming problem where the objective is to minimize the cost of chicken and grain while satisfying the protein and fat requirements.
Let's define:
- x as the ounces of chicken.
- y as the ounces of grain.
Objective Function:
Minimize Cost = 9x + y (since chicken costs 9 cents/oz and grain costs 1 cent/oz)
Constraints:
1. Protein: 10x + 2y ≥ 226 (at least 226 grams of protein)
2. Fat: 5x + 2y ≥ 166 (at least 166 grams of fat)
Solving this Linear Programming problem typically requires graphical methods or utilizing software like Excel Solver or a programming language library designed for optimization. The solution will give the optimal amounts of chicken and grain in ounces to be used in each bag of dog food to minimize cost while meeting the nutritional requirements.
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