Question 1146716
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.


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