PCMI, Summer 2004
High School Teacher Program

Forester Problem

A forester has a piece of land with 3000 Christmas trees that were in three classes of height: small, medium and large. Just before Christmas, he cuts a number of trees to sell them. The small trees are not worth anything yet, the medium ones sold for $10, and the larger ones for $25. He had 1000 small, 1000 medium and 1000 large trees. The trees grow in this way: 40% of the small become medium, 20% of the medium become large.

What is the composition of the forest just before next Christmas? If after cutting medium and large trees and planting small trees he wants his starting population back, how many of each kind should be cut and planted? Cutting one tree costs $1.00 and planting one tree cost $2. What is his profit?

The forester has three strategies to cut his trees:
    a) Cut after one year and plant to get your starting population back
    b) Cut after two years and plant to get your starting population back
    c) Cut after one year only enough large trees to keep 1000 large trees and replant the same number of small trees. Repeat this the second year.

Which of the strategies is most profitable per year?

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