Question 1076461



your 2 inequalities are:


3x + 4y <= 50


2y <= 3x + 13


the second equation can be shown as:


-3x + 2y <= 13


solve the equality portion of these 2 inequalities.


those are the following equations:


3x + 4y = 50

-3x + 2y = 13


add these equations together and you get:


6y = 63


solve for y to get y = 10.5


that appears to be a break even point.


that value of y has to satisfy both inequalities.


when y = 10.5, the first inequality is solved as follows:


3x + 4y <= 50


replace y with 10.5 and the inequality becomes:


3x + 42 <= 50


solve for x to get x <= 2.67


when y = 10.5, the second inequality is solved as follows:


-3x + 2y <= 13


replace y with 10.5 and the inequality becomes:


-3x + 21 <= 13


solve for x to get x >= 2.67


this indicates that, when y = 10.5, x has to be equal to 2.67.


both constraints are satisfied.


it remains to be tested for y > 10.5 and for y < 10.5


you can pick any values of y < 10.5 and any values of y > 10.5


i picked y = 5 and y = 20


when y = 5:


3x + 4y <= 50 tells you that x has to be <= 10.


and:


-3x + 2y <= 13 tells you that x has to be >= -1.


since x can't be negative, then x has to be >= 0.


both inequalities are satisfied when y = 5 which is less than y = 10.5


when y = 20:


3x + 4y <= 50 tells you that x has to be <= -10.


since this is impossible, then you can assume that y can't be >= 10.5