Give your answer rounded to the nearest whole number.

Question

A farmer finds that if she plants 45 trees per acre, each tree will yield 30 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest?

___________ trees



Answer 1

The key here is to get the formula correct.

(x+45)(30-4x) will yield the maximum amount trees per acre that will yield 4 more bushels per acre than today's yield.

F(x) = (x+45)(30-4x)

= 30x - 4x^2 + 1350 - 180x

= -4x^2 - 150x - 1350 This a a parabola that opens downward.

The maximum point is (-18.75, 2756.25)

which means he should subtract 19 trees per acre that will yield the maximum yield

or 26 trees per acre.