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A farmer has $70$ acres on which to plant a pear orchard. three neighboring farms with similar soil conditions already established orchards. one of these orchards has $250$ tress planted per acre yielding, on average, $525$ pears per tree. Another $280$ trees per acre, yielding $480$ pears per tree, while the third with $350$ tress per acre yields only $375$ pears pear tree.

Based on the data, derive equations for both the yield per tree and the yield per acre as functions of $x$, the tree density(trees/acre). What density of planting is expected to yield no pears? What density does your model suggest will produce the maximum yield per acre.

The average weight of a pear is approximately $1/2$-pound. Using appropriate transformation write an equation expressing the total yield from the farmer's $70$ acres, measured in tons(rather than pears), as a function of the number of tress per acre( NOTE: $1$ u.s ton=$2,000$ pounds).

the equation i got for the first part is. y= -1.5x+900

when the density of planting is 600 it is expected to yield no pears

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  • $\begingroup$ the equation i got for the first part is. y= -1.5x+900 $\endgroup$ – Alain Michel Sep 27 '15 at 16:39
  • $\begingroup$ when the density of planting is 600 it is expected to yield no pears $\endgroup$ – Alain Michel Sep 27 '15 at 16:40
  • $\begingroup$ when the density is 0 the model suggest it will produce the maximum yield per acre $\endgroup$ – Alain Michel Sep 27 '15 at 16:41
  • $\begingroup$ How do i come up with an equation that is in tons rather than pears? $\endgroup$ – Alain Michel Sep 27 '15 at 16:57
  • $\begingroup$ First, you should put these comments in the body of the question. Second, you are incorrect about the maximum yield per acre: when the density is $0$, you get the maximum yield per tree, but you have no trees, so the yield per acre is zero. The yield per acre is $x$ times the yield per tree, i.e. $x(-1.5x+900)$. $\endgroup$ – Ian Sep 27 '15 at 17:09

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