Solve the system of equations. – 5x + 2y = 9 y = 7x X = Y =
2 answers:
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Answer:
Lets denote
1. eggs as x,
2. edamame as y
3. elbow macaroni as z
The problem then is
min TC=2x+5y+3z
subject to
Step-by-step explanation:
First the objective is to minimize total cost subject to some nutritional requirements.
So the total cost function (TC) is the number of servings multiplied for the corresponding costs. Eggs cost 2, edamame 5, and macaroni 3
Next we have to meet the nutritional requirements, the first of the restrictions is the protein restriction. The problem requires that the meal contains at least 40g of carbohydrates (that is why the restriction is ). Then we add how much each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.
Same for protein, we need at least 20 grams of protein (). Eggs add 17g, edamame adds 12g, and macaroni adds 8g.
Finally we don't want more than 50 grams of fat (). Eggs add 14g, edamame add 6g and macaroni 1g.
Finally, we add the non negativity restrictions-> we cannot buy negative quantities of these goods, but we allow for zero.