3. The Charm City Cereal Company makes a cereal from several ingredients. Two of

Question

3. The Charm City Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 55 milligrams of vitamin A and 30 milligrams of vitamin B while minimizing the total cost. An ounce of oats contributes 8.25 milligrams of vitamin A and 1.20 milligram of vitamin B, whereas an ounce of rice contributes 6.40 milligrams of vitamin A and 2.30 milligrams of vitamin B. An ounce of oats costs $0.14, and an ounce of rice costs $0.10.

Explanation / Answer

Answer: Suppose O be the ounces of Oats and R be the ounces of Rice.

A and B are the vitamins given by these two commodities.

The solution to the given problem can be achieved through Linear programming Model as follows:

We want to minimize the costs as follows:

Minimize z = $0.14O + $0.10R

Subject To:
8.25O + 6.40R >= 55
1.20O + 2.30R >= 30
O >= 0
R >= 0

This Model is used for serving purpose only. The final amount in each box may depend on total number of servings put into a box.

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