WALNUT TREE PROBLEM
A walnut grower estimates from past records that if 20 trees are planted per acre, each
tree will average 60 pounds of nuts per year. If for each additional tree planted per acre
(up to 15) the average yield per tree drops 2 pounds, how many trees should be planted to
maximize the yield per tree? What is the maximum yield?
SOLUTION:
Let x = # of additional trees planted/acre
20 + x = # of trees planted/acres
60 – 2x = yield/tree
Yield/acre = (trees/acre)(yield/tree)
Domain given: [0, 15]
Y(x) = (20 + x)(60 – 2x) = 1200  20 x  2 x 2
MAXIMIZE: Y ( x)  20  4 x
4x = 20
x = 5 (note only one c.v.)
CHECK: Y ( x)   4  0 (ABS. MAX.)
# trees planted = 20 + 5 = 25
Maximum yield = Y(5) = (25)(50) = 1250 lbs/acre