Question

Find the maximum and minimum values by evaluating the equation C=2x+y at the critical points if the restrictions are the following:
X>=0
Y>=4
X+Y<=8

Answer 1

I don't think such function have critical points. I suspect (4,4) is the maximum and (0,4) is the minimum though. Take it with a lot of salt.

Answer 2

lol thanks

Answer 3

For maximum, you clearly what to use the biggest x and y possible. So x+y=8. Furthermore, you want to use the biggest x possible because C=2x+y and hence the smallest y possible. The smallest y you can use is 4 and so the biggest x you can use is 4, so the maximum is (4,4).

For the minimum, you want to use the smallest x and y possible. So x=0 and y=4. x=0 and y=4 satisfy x+y<=8 so you are good to go.