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Expert: - 6/8/2008


Question
I have no clue where to start....Here is the question.. An apple orchard now has 80 trees planted per hectare and the average yield per tree is 400 apples. For each additional tree planted per hectare, the average yiel per tree is reduced by approximately four apples. How many tree per hectare wil give the largest crop of apples?

Answer
If we have 80 trees, the production is 400 apples / tree.
Looking at the units, these would need to be multiplied to get the total apple production.

An increase of 1 tree would mean a decrease of 4 apples/tree.  
An increase of 2 trees would mean a decrease of 8 apples/tree.  
An increase of n trees would mean a decrease of 4n apples/tree.

The equation to use would be 80+n trees with a production of 400-4n apples.  Multiply these two together, find the derivative, and set the derivative equal to 0, then solve.

The result is n, but we are looking for the total trees.  Looking back at the problem, note that equation for the total trees is 80+n.

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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