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Answer:
The beam initial temperature is 5 °F.
Step-by-step explanation:
If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that
where is the ambient temperature, is the initial temperature, is the time and is a constant yet to be determined.
The goal is to determine the initial temperature of the beam, which is to say
We know that the ambient temperature is , so
We also know that when the temperature is and when the temperature is which gives:
Rearranging,
If we divide these two equations we get
Now, that we know the value of we can use it to find the initial temperature of the beam,
so the beam started out at 5 °F.
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.