SOLUTION: My group and I tried to work on this one and ended up with A(t)= -1.5t^2 + 900t + 0 but I dont think that is correct. Any help you could give me would be greatly appreciated!

Question 182648: My group and I tried to work on this one and ended up with A(t)= -1.5t^2 + 900t + 0 but I dont think that is correct. Any help you could give me would be greatly appreciated!

Farmer Bill has 70 acres on which he wants to plant a pear orchard. Three neighboring farms with similar soil conditions already have established orchards. Based on the yield from the neighboring farms, the yield per tree appears to be a linear function of the tree density (trees per acre). Letting �t� be the number of trees planted per acre, the function P(t)= -1.5t + 900 represents the yield in pears per tree.
What function of �t� would then give the yield per acre for the orchard? Assuming Farmer Bill wants to maximize his yield, what is the optimal number of trees to plant per acre, and what will be the total yield from the farmers 70 acre orchard?

1. Write an equation for the yield per acre as a function A(t)
2. Absolute minimum or absoulte maximum?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Farmer Bill has 70 acres on which he wants to plant a pear orchard. Three neighboring farms with similar soil conditions already have established orchards. Based on the yield from the neighboring farms, the yield per tree appears to be a linear function of the tree density (trees per acre). Letting �t� be the number of trees planted per acre, the function P(t)= -1.5t + 900 represents the yield in pears per tree.
What function of �t� would then give the yield per acre for the orchard? Assuming Farmer Bill wants to maximize his yield, what is the optimal number of trees to plant per acre, and what will be the total yield from the farmers 70 acre orchard?
1. Write an equation for the yield per acre as a function A(t)
A(t) = t*(900 - 1.5t) the # of trees times the pears/tree
2. Absolute minimum or absoulte maximum?
A(t) = 900t - 1.5t^2
dA/dt = 900 - 3t = 0
t = 300
There's another way to find max and min of a parabola, but I don't know what it is. It's based on the value of y at the vertex.
------------------
For 70 acres:
Each acre is 900*300 - 1.5*300*300
Yield = 135,000*70 = 9,450,000 pears, and it's a maximum

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