Homework SourseAn ugli fruit grower finds that if he plants 27 trees per ac
An ugli fruit grower finds that if he plants 27 trees per acre, each tree will yield 62 bushels of ugli fruit. He also estimates that for each additional tree that he plants per acre, the yield of each tree will decrease by 2 bushels. How many trees should he plant per acre to maximize his harvest and what is the maximum harvest?
An ugli fruit grower finds that if he plants 27 trees per acre, each tree will yield 62 bushels of ugli fruit. He also estimates that for each additional tree that he plants per acre, the yield of each tree will decrease by 2 bushels. How many trees should he plant per acre to maximize his harvest and what is the maximum harvest?
Solution
if he plants 27 trees per acre, each tree will yield 62 bushels of ugli fruit
for each additional tree that he plants per acre, the yield of each tree will decrease by 2 bushels.
So, let x additional plants are planted per acre: (27 +x)
Decrease in yield for x additional plants planted : 2x
So, yield after decrease ( 62 -2x)
So Total yeild = no. of trees x yiled per plant = ( 27 +x)( 62 -2x)
F(x) = ( 27 +x)( 62 -2x) = 1674 -54x +62x -2x^2
= -2x^2 +8x +1674
At maximum yield , dF/dx =0 ; -4x +8 ---> x= 2
No. of trees = ( 27 +2) = 29
maixium yield = (27+2)(62 -2*2) = 1682 brushels
