Question

The annual yield per lemon tree is fairly constant at 320 pounds when the number of trees per acre is 50 or fewer. for each additional tree over 50, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. find the number of trees that should be planted on an acre to produced the maximum yield. help!!!!!!!

Answer 1

X=15 AND THE MAX YIELD IS 16900 BUT I DONT KNOW HOW TO DO THE LAST PART?

Answer 2

x = +15 trees over 50 (65) gives max yield per acre THATS ALL I KNOW

Answer 3

WHOEVER HELPS ME I'LL WRITE THEM A TESTIMONIAL

Answer 4

HELP!!!!!!!!

Answer 5

I NEED HELP REAL TALK I ALREADY DID EVERYTHING BUT IDK HOW TO FIND THE LAST PART ONLY>.<

Answer 6

WOULD IT BE 3250 OR JUST 65?

Answer 7

OR IS IT 15?

Answer 8

Let x = number of trees (over 50). So x > 50.


So if x > 50, then we start losing lemons (4 lbs at a time). So the total yield is


x*(320 - 4(x-50))


Expand and simplify


x*(320 - 4x + 200)


x*(520 - 4x)


520x - 4x^2


-4x^2 + 520x


Now complete the square


-4x^2 + 520x


-4(x^2 - 130x)


-4(x^2 - 130x + 4225 - 4225)


-4((x - 65)^2 - 4225)


-4(x - 65)^2 + 16900

Answer 9

The last line, -4(x - 65)^2 + 16900, tells us that when x = 65, the production peaks at 16,900 lbs

So you should plant 65 trees to get a maximum yield of 16,900 lbs of lemons

Answer 10

THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111

Answer 11

np