An ugli fruit grower finds that if he plants 27 trees per acre, each tree will y

Question

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?

Explanation / Answer

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.