The Munchies Cereal Company makes a cereal from several ingredients. Two of the

Question

The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company want to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs $0.05 and an ounce of rice costs $0.03. Use the description in Scenario 2. Which constraint below is a part of the LP formulation for the problem? 1x_1 + 2x_2 greaterthanorequalto 12 2x_1 + 1x_2 lessthanorequalto 48 6x_1 + 2x_2 greaterthanorequalto 48 0.05x_1 + 0.03x_2 greaterthanorequalto 12

Explanation / Answer

Solution:

Let x1 be the ounces of Oats and x2 be the ounces of Rice in a serving

to minimize cost let z

z =  z = $0.05x1 + $0.03x2

subject to given constraint

for vitamin A

8x1 + 6x2 48

for vitamin B

1x1 + 2x2 12

x1 , x2 0

Now as we can see that

1x1 + 2x2 12 is the part matching with given constraint

therefore option (1) 1x1 + 2x2 12 is correct '

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