SOLUTION: Hi tutor, Can you help me solve the following word problem? A farmer grows rutabagas in a field of 8 hectares. He could harvest the crop now and get 3t/ha, which will sell f

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Question 800341: Hi tutor,
Can you help me solve the following word problem?
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?
So far I have this:
let x be the number of weeks he waits.
price= 200-10x
yield= 3-0.3x
Can u help me with what I should do next.
Thanks
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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 =
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