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Calculus/Optimization Calculus

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Question
A florida orange grower finds that the average yield/tree is 400 oranges, if no more than 16 trees are planted in each plot. For each additional tree per plot the yield of each tree is decreased by 20 oranges. How many trees should be planted in each plot to maximize yield?

Answer
Let t be the number of trees planted.
The number of oranges per tree will be
400 - 20 (t - 16) =

720 - 20t


So the total yield will be

y  = (t)(720-20t)

y = 720t - 20t^2

y' = 720 - 40t

0 = 720 - 40t

40t = 720

4t = 72

t = 18

So planting 18 trees gives maximum yield  

Calculus

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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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Ph.D. in Mathematics and many years teaching Calculus at state universities.

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