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A food scientist is developing a new recipe. He needs it to have between 2 and 4 teaspoons of sugar per serving and between 1 and 4 grams of fiber. Each teaspoon of sugar has 5 carbohydrates. Each gram of fiber counts as a carbohydrate when counting total carbohydrates. If the recipe already has 12 carbohydrates per serving from other sources, create a linear programming feasible region to minimize the total carbohydrates in the recipes nutrition profile.

A food scientist is developing a new recipe. He needs it to have between 2 and 4 teaspoons-example-1
User NickC
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1 Answer

21 votes
21 votes

SOLUTION:

We are told that, the scientist wants it to have between 2 and 4 teaspoons of sugar per serving and between 1 and 4 grams of fiber.

Let the spoons of sugar be x and the grams of fiber be y;

We can write in mathematical terms;


\begin{gathered} 2\le x\le4 \\ \text{and} \\ 1\le y\le4 \end{gathered}

We also told that, each teaspoon of sugar has 5 carbohydrates. Each gram of fiber counts as one carbohydrate.

Plotting this inequality on a graph, we get a region of possible combinations of sugar and fiber.

The combinations which minimize or maximise such combinations are usually the vertices of the resulting polygon,

Here, the minimum selection is (2,1) which means, that.

The minimun number of carbohydrates per serving occurs when the recipe has;

2 teaspoons of sugar per serving

1 gram of fiber per serving

Therefore, the minimum number of carbohydrates per serving in the recipe will be.


\begin{gathered} (2*5)+(1*1)+12(\text{from other sources)} \\ =10+1+12 \\ =23\text{ } \end{gathered}

Therefore, the minimum number of carbohydrates per serving in the recipe will be 23 carbohydrates,

A food scientist is developing a new recipe. He needs it to have between 2 and 4 teaspoons-example-1
User Onknows
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