Let x be the number of additional trees planted per acre
Number of trees per acre = 30+x
yield per tree = 150 - 3x
total = (30+x)(150-3x)
= 4500 + 60x - 3x^2
d(total)/dx = 60 -6x
=0 for a max total
6x=60
x = 10
So the max yield is obtained with 40 trees per acre.
BUT, your condition says that the number of trees per acre is ≤ 30
So I guess 30 would be the max
(strange question!)
When 30 orange trees are planted per acre each tree yields 150 oranges For each additional
tree per acre, the yield decreases by 3 oranges per tree. Express the total yield of oranges per
acre, Y , as a function of the number of trees planted per acre, x, if x �< or equal to 30.
6 answers
the answer they give is y=240x -3x^2 and i have no idea how they got that because i did get the y=4500 +60x-3x^2 as my answer and that is a choice but its not the correct one.
Looks like you defined x as the number of extra trees to be planted, which is what I did as well
They defined x as the actual number of trees planted.
When you differentiate their equation , set it equal to zero and solve you get x = 40
the total number of trees is 40
Notice that is exactly the same answer that I got.
But then the question said that the x ≤ 30, so the max is 30
As I said before, this is a dumb question.
They defined x as the actual number of trees planted.
When you differentiate their equation , set it equal to zero and solve you get x = 40
the total number of trees is 40
Notice that is exactly the same answer that I got.
But then the question said that the x ≤ 30, so the max is 30
As I said before, this is a dumb question.
x is suppose to be the number of trees planted per acre,
oh sorry i see now. thanks!
Ok, let's do it their way, (and get the same answer as I got before)
Let the number of actual trees planted be k
(I will now switch my original definitions to this new definition)
number of trees = k , I had x+30
so k= x+30 and x = k-30
yield per acre:
I had 150-3x
= 150 - 3(k-30)
= 150- 3k +90
= 240 - 3k
total yield = k(240-3k)
= 240k - 3k^2
heh, I simply used k instead of their x
so yield = 240x - 3x^2
(remember my use of x is not the same as their use of x )
This will produce a maximum value of x = 40
for a maximum number of trees as 40 per acre, the same as before in my first reply.
But, again, they said there was a max of 30, which is what the original was.
So again, dumb question.
Let the number of actual trees planted be k
(I will now switch my original definitions to this new definition)
number of trees = k , I had x+30
so k= x+30 and x = k-30
yield per acre:
I had 150-3x
= 150 - 3(k-30)
= 150- 3k +90
= 240 - 3k
total yield = k(240-3k)
= 240k - 3k^2
heh, I simply used k instead of their x
so yield = 240x - 3x^2
(remember my use of x is not the same as their use of x )
This will produce a maximum value of x = 40
for a maximum number of trees as 40 per acre, the same as before in my first reply.
But, again, they said there was a max of 30, which is what the original was.
So again, dumb question.
4 answers