Expert: Scott A Wilson - 11/21/2010

Question
a hog raiser can sell  100 pigs  of average weight  of 80 kilos each at a profit of  $1 per kilo if sold immediately. past experience
had taught him that for every one week delay in selling the pigs, his pigs shall gain 0.9 kilo per week per pig. meantime, profit shall
also decreased by 1/1oo of a dollar per  week. now, the hog raiser wishes to find out the number of weeks he may delay selling yet realizing the same original profit

Answer
The price is $1 per kilo, and decreases by a penny for each week.
Let n be the number of weeks, so the price is 1.00 - 0.01n.

The weight starts at 80, and goes up by 0.9 for each week,
so the weight is given by 80+0.9n.

Together, these make the sale price at P(n) = (1.00-0.01n)(80+0.9n).
Setting this equal to 80 will find when the price is equal again.

So 80 = (1-0.01n)(80+0.9n).
Multiply this out, subtract 1 from both sides, and note that 80 can be subtracted from both sides.  The right sides can then be factored with two solutions.  They will be n = 0 and n around 10 (or so).
That means they start selling at $80 and after a little over 10 weeks they are back to $80.

Since this is parabolic, the maximum is halfway between these two solutions, so somewhere over 5.