A YELLOW POPLAR PROBLEM (N. C). 



PREMISES : A careful tally of the yellow poplar trees, stand- 

 iug in the valley drained by Claw Hammer creek, furnishes the fol- 

 lowing data : 

 1090 trees of i}^ foot diameter, containing 300 feet b. m. each, 



equal to 327,000 feet b. m. 



1980 trees of 2 foot diameter, containing 450 feet 



b. m. each, equal to 891,000 " " 



860 trees of 2J^ foot diameter, containing 700 



feet b. m. each, equal to 602,000 " " 



680 trees of 3 foot diameter, containing 1000 feet 



b. m. each, equal to 680,000 " " 



270 trees of over zyi foot diameter, containing 



1700 feet b. m. each, equal to 459,000 " " 



The stumpage of these trees is worth, on an average. 

 In the case of trees of i^ foot diameter, . $0.75 per 1000 feet b. m. 

 In the case of trees of 2 foot diameter, . . 1.25 per 1000 feet b. m. 

 In the case of trees of 2}i foot diameter . 2.50 per 1000 feet b. m. 

 In the case of trees of 3 foot diameter . . 4.25 per 1000 feet b. m. 

 In the case of trees of over 3^ foot diameter 6.25 per 1000 feet b. m. 



The trees, up to zyi foot in diameter, are growing at a rate of 

 lyi inches in 10 years, and thereafter at a rate of i inch in 10 years. 



The taxes are not apt to be reduced after the timber is cut. 



The owner believes, that the price of poplar stumpage will 

 double in 25 years (annual increase of 2;^ per cent), and is satisfied 

 to make 5 per cent on the investment. 



QUESTION : At what rate shall the owner dispose of the 

 trees, viz. down to what diameter limit is it advisable for him to 

 sell the trees 7 



POINTS : 



1. AtreeofiJ^footdiameter,in4oyears, attains 2 footdiameter 

 A tree of 2 foot diameter, in 40 years attains . . 2^ foot diameter 

 A tree of 2% foot diameter, in 60 years attains. . 3 foot diameter 

 A tree of 3 foot diameter, in 60 years attains . . . 3}4 foot diameter 



2. The t}4 foot tree, now worth $0.75 x 0.300 = 22}4 cents, 

 will be worth after 40 years $1.25 x 0.450 x 1.025" = . . . $ 1.52 

 The 2 foot tree, now worth $1.25 x 0.450 = 56 cents, will be 



worth after 40 years $2.50 X 0.700 X 1.025^ = . ... 4.72 

 The 2>^ foot tree, now worth $2.50 x 0.700= 175 cents, will 



be worth after 60 years $4.25 x i.ooo x 1.025'" = . . . 18.70 

 The 3 foot tree, now worth $4.25 x i.ooo = 425 cents, will be 



worth after 60 years $6.25 x 1.700 x 1.025*' = . . . . 46.80 



3. All trees, growing at a 5 per cent, rate, are to remain ; those 

 growing at a rate of less than 5 per cent, will be cut. 



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