<PRE><B>Question 800341</B>
A farmer grows rutabagas in a field of 8 hectares.
 He could harvest the crop now and get 3t/ha, which will sell for $200/t.
 Each week the farmer waits, the yield will increase by 0.3t/ha but the price will drop by $10/t. When should the farmer harvest his rutabagas to get maximum return? 
:
Let w = no. of week to harvest
f(w) = (3 + .3w)(200 - 10w)
FOIL
f(w) = 600 - 30w + 60w - 3w^2 
y = f(w)
y = -3w^2 + 30w + 600
A quadratic equation, the axis of symmetry; x will be max y Use x = -b/(2a)
x = {{{(-30)/(2*-3)}}}
x = +5 weeks will give max return
that would be
(3+1.5)(200-50) = 675 max return
If he sold right now only
3 * 200 = 600</PRE>