SOLUTION: In a 6 acre apple orchard, it is decided to plant 20 or more trees per acre. If 20 trees are planted per acre then each mature tree will yield 200 apples per year. For each additio

Question 1146716: In a 6 acre apple orchard, it is decided to plant 20 or more trees per acre. If 20 trees are planted per acre then each mature tree will yield 200 apples per year. For each additional tree planted per acre, the number of apples produced by each tree decreases by 12 per year. Express the total number of apples A produced per year in terms of the number n of trees per acre.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe your formula will be:

y = 6 * (20 + x) * (200 - 12 * x)

there are 6 acres and each acre will produce (10 + x) * (200 - 12 * x) apples.

x represents the number of additional trees per acre.

when x = 0, each acre will produce 20 * 200 = 4000 apples and 6 acres will produce 6 * 4000 = 24000 apples.

when x = 1, each acre will produce 21 * 188 = 3948 apples and 6 acres will produce 6 * 3948 = 23688 apples.

when x = 10, each acre will produce 30 * 80 = 2400 apples and 6 acres will produce 6 * 2400 = 14400 apples.

based on this formula, the maximum number of apples produced is when x = -(1 + 2/3).
when x = -(1 + 2/3), each acre will produce (20 - (1 + 2/3)) * (200 + 12 * (1 + 2/3)) = 4033 + 1/3 apples and 6 acres will produce 24200 apples.
that comes out to be (18 + 1/3) apple trees per acre times 220 apples per tree = (4033 + 1/3) apples per acre times 6 = 24200 apples for the whole orchard.

this can be seen in the following graph.
the blue line is the results for each acre.
the red line is the results for 6 acres.

$$$

RELATED QUESTIONS
Each orange tree grown in California produces 630 oranges per year if not more than 20... (answered by Boreal,ikleyn)

Each orange tree grown in California produces 630 oranges per year if not more than 20... (answered by ikleyn)

The owner of the local apple orchard estimates that if 24 trees are planted per acre,... (answered by ikleyn,Theo)

PLEASE HELP ME WITH THIS PROBLEM< ITS MY LAST ONE AND I'M STUCK!!!! ***I NEED THE... (answered by ankor@dixie-net.com)

A farmer finds that if she plants 95 trees per acre, each tree will yield 30 bushels of... (answered by greenestamps)

A farmer finds that if she plants 80 trees per acre, each tree will yield 65 bushels of... (answered by ikleyn)

My group and I tried to work on this one and ended up with A(t)= -1.5t^2 + 900t + 0 but I (answered by Alan3354)

An orange grower finds that she gets a yield of 40 bushels of oranges per tree when she... (answered by stanbon)