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
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-> 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
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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):
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.
