Question 74512
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 + 110M}}}
{{{165 <= C <= 330}}}
from these I get
{{{165 <= 165E + 110M}}}
{{{165E + 110M <= 330}}}
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{{{1 <= E + (2/3)M}}}
{{{E + (2/3)M <= 2}}}
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{{{E >= 1 - (2/3)M}}}
{{{E <= 2 - (2/3)M}}}
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I plot these inequalities with E on the vertical axis
and M on the horizontal axis
{{{ graph( 500, 500, -1, 3, -1, 3, 1 - (2/3)x , 2 - (2/3)x) }}}
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 >= 1 - (2/3)M}}}
{{{(2/3)M >= 0}}}
{{{M >= 0}}}
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{{{1 <= 2 - (2/3)M}}}
{{{(2/3)M <= 2 - 1}}}
{{{M <= 3/2}}}
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So, if the patient has 1 egg, they are allowed between
no meat and 1.5 ounces of meat.