SOLUTION: I am having a hard time with this question, Please help me understand how to get the answer, I am not even sure where to start with this one. Suppose that you are a hospital dieti

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Question 74512: I am having a hard time with this question, Please help me understand how to get the answer, I am not even sure where to start with this one.
Suppose that you are a hospital dietician. A patient must have at least 165 milligrams and no more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol and each ounce of meat provides 110 milligrams of cholesterol.

Graph the system of inequalities in the first quadrant (explain why). Identify at least two ordered pairs that are part of the solution set. Describe what each ordered pair means in terms of the variables for this problem.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
E = number of eggs per patient per day
M = ounces of meat per patient per day
C = milligrams allowed cholesterol per patient per day
C+=+165E+%2B+110M
165+%3C=+C+%3C=+330
from these I get
165+%3C=+165E+%2B+110M
165E+%2B+110M+%3C=+330
------------------------
1+%3C=+E+%2B+%282%2F3%29M
E+%2B+%282%2F3%29M+%3C=+2
---------------------
E+%3E=+1+-+%282%2F3%29M
E+%3C=+2+-+%282%2F3%29M
---------------------
I plot these inequalities with E on the vertical axis
and M on the horizontal axis
+graph%28+500%2C+500%2C+-1%2C+3%2C+-1%2C+3%2C+1+-+%282%2F3%29x+%2C+2+-+%282%2F3%29x%29+
The solutions lie between and including the parallel lines
If fractional parts of an egg are allowed
(M,E) represents a solution set obeying the inequalities
If E = 1,
1+%3E=+1+-+%282%2F3%29M
%282%2F3%29M+%3E=+0
M+%3E=+0
---------------
1+%3C=+2+-+%282%2F3%29M
%282%2F3%29M+%3C=+2+-+1
M+%3C=+3%2F2
----------------
So, if the patient has 1 egg, they are allowed between
no meat and 1.5 ounces of meat.