A squash patch currently has 120 lbs of butternut squash. For each additional day in the patch, the amount of butternut squash increases by 6 lbs. If the price of butternut squash is currently 80 cents per pound, but it decreases by 2 cents each day, how long should the butternut squash grow to maximize profit?

Question

Steve · Accepted Answer

after x days, we have

lbs: 120 + 6x
price: .80-.02x

No idea about profit, since cost was not mentioned, but the income is certainly

(120+6x)(.80-.02x) = -0.12x^2 + 2.4x + 96

That is just a parabola with vertex at (10,108)

Bob · Answer

10 days, because the x of the vertex is the maximum profit

QWERTY · Answer

thanks

nia · Answer

@Steve, where does the -0.12x^2 + 2.4x + 96 come from? I don't understand, please answer

Jeff · Answer

it is from (120+6x)