Math Help Quadratics
August 17th, 2010
Question: Math Quadratics Help!!!!?
Please help with this quadratics question!
A farmer grows rutabagas in a field of 8 hectares, he could harvest the crop now and get 3t/ha which would 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 for maximum return?
I know i need to complete the square, but i need to find an equation for that question! so plz help me come up with an equation.
Thanks!! 
Answer: Let x be the number of weeks the farmer waits.
The farmer can expect the yield to be (3 + 0.3x) t/ha.
He can expect the price to be (200 – 10x) $/t.
So his return will be
(3 + 0.3x)(200 – 10x) $/ha.
That is,
-3x^2 + 30x + 600 $/ha
This is a quadratic with negative leading coefficient, so it has an absolute maximum where its first derivative -6x + 30 vanishes. That is at x=5.
The farmer should harvest his rutabagas at 5 weeks.
Algebra Help – The Quadratic Formula – YourTeacher.com
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