Toronto Math Forum

The following is my sample answer for quiz 2.

This is my answer for quiz 1.

The following is the sample for quiz 4.

The following is the sample of quiz2.

Yes, it can be solved using Lagrange multiplies. However note, if restrictions are $g_1\le 0$, $g_2\le 0$, $g_3\le 0$ you need to consider

• $g_1=0$ (and $g_2\le 0, g_3\le 0)$); there will be only one Lagrange multiplier at $g_1$. Two other cases in the similar way
• $g_1=g_2=0$ (and $ g_3\le 0)$); there will be  two Lagrange multipliers. Two other cases in the similar way

It will be, however, more cumbersome. Note that (1) corresponds to two rays and one arc, (2) to two corners.

No, you need not consider quadratic forms after you found all suspicious points. It would serve no purpose.