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I'm sorry I could not upload my homework because I'm too new to post images. The image can be obtained here: http://i40.tinypic.com/2u5rl80.png.

I'm also sorry to ask such a big question. The instructor didn't provide enough materials in class for me to do the homework myself, so I don't even have any idea how to start. I don't need a complete solution, any helpful hint would be good. But if I could not proceed though I've tried based on the hint, I will continue to ask. So I hope I could get help in an interactive manner. Thank you very much for any help!

user76300
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  • It appears that others have deleted comments you responded to. I'd suggest that you also delete your now dangling comments (using the cross that appears at the end if you hover over them) since they're distracting from the question. If some of the material in the comments is still relevant, you can incorporate it into the question instead. (There's an edit link underneath the question.) – joriki May 06 '13 at 05:35
  • If the questions look too abstract, try to see (to draw) what happens in dimension 2, and generalize. For instance, for (a): What happens if the affine set is empty? in the same direction as the (level lines of the) constraint? not in the same direction? – Vincent Zoonekynd May 06 '13 at 07:33

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