<PRE><B>Question 1183271</B>
&lt;br&gt;
a) Solve P=0:&lt;br&gt;
{{{-2k^2+12k-10=0}}}
{{{k^2-6k+5=0}}}
{{{(k-1)(k-5)=0}}}
{{{k=1}}} or {{{k=5}}}&lt;br&gt;
ANSWERS: The profit is 0 when k is 1 or 5 -- that is, when either 1000 or 5000 key rings are produced per day.&lt;br&gt;
b) Using the symmetry of the parabolic graph, the maximum profit is when k is halfway between the two zeros of 1 and 5 -- i.e., when k=3.&lt;br&gt;
ANSWER: The maximum profit is when 3000 key rings are produced per day.&lt;br&gt;
c) The maximum profit is P(3):&lt;br&gt;
{{{-2(3^2)+12(3)-10 = -18+36-10 = 8}}}&lt;br&gt;
ANSWER: The maximum profit is 8000 dollars</PRE>