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songoku
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Homework Statement
Sketch the area that fulfills :
x + y ≥ 1
3y ≥ 2x - 1
2y ≤ 3x
and find the range of x and y that are restricted.
Find the maximum value of y – 2x that satisfies the area above and find also the value of x
Homework Equations
Line equation
The Attempt at a Solution
I've drawn the graph and got :
I'm not sure about finding the range of x and y that are restricted. Do I have to find the value of x and y that are allowed or not allowed ?
And I don't think that the answer can stated in specific range for x and y. If I want to find the range of x that is allowed, I can't state that [tex]x\geq 0.4[/tex] satisfies the inequalities because there are values of [tex]x\geq 0.4[/tex] where (x,y) lie outside the shaded area.
I can state that [tex]x\leq 0.4[/tex] is not allowed, but there are some values of [tex]x\geq 0.4[/tex] that are also not allowed...
For maximum value of y - 2x, I substitute (0.4 , 0.6) to get maximum value -0.2
But I don't know how to give an argument that this is the maximum value..
Thanks
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