A company mixes oats and rice to make cereal. Each box of cereal must provide 48

Question

A company mixes oats and rice to make cereal. Each box of cereal must provide 48 milligrams of Vitamin A and 12 milligrams of vitamin B, while minimizing the cost of making the box. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B. An ounce of rice contributes 6 milligrams of vitamin A and 2 milligrams of vitamin B. Let X1 = ounces of oats in the box and X2 = ounces of rice in the box. A linear program is formulated to minimize cost while meeting the requirements for vitamins A and B. Which of the following statements is true?

A. 8X1 + X2 <= 12 is a constraint

B. 8X1 + X2 >= 12 is a constraint

C. X1 + 6X2 <= 48 is a constraint

D. The problem cannot be solved optimally with the information provided

Explanation / Answer

Constraint for vitamin A:

8X1 + 6X2 >= 48

Constraint for vitamin B:

X1 + 2X2 >= 12

So you can see that the option A, B, and C are wrong.

Now to minimize the cost we will need the price of rice and oats, So

The correct option is D.

The problem cannot be solved optimally with the information provided

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