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 45 milligrams of vitamin A and 20 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8.5 milligrams of vitamin A and 1.2 milligram of vitamin B, whereas an ounce of rice contributes 6.4 milligrams of A and 2.2 milligrams of B. An ounce of oats costs $0.08, and an ounce of rice costs $0.05.

Formulate a linear programming model for the above situation by determining
(a) The decision variables.
(b) The objective function.
(c) All the constraints.

Explanation / Answer

amount of oats = X ounce
amount of rice = Y ounce
minimum vitamin A requirement = 45 mg
minimum vitamin B requirement = 20 mg

An ounce of oats contributes 8.5 milligrams of vitamin A and 1.2 milligram of vitamin B.
An ounce of rice contributes 6.4 milligrams of vitamin A and 2.2 milligrams of vitamin B.

a) Decision variables = X , Y

b) objective fuction ,

minimize Z = 0.08X + 0.05Y

c) constraints , 
=> 8.5X + 6.4Y >= 45

    1.2X + 2.2Y >= 20

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