Expert: Ahmed Salami - 4/21/2009

Question
Hey Mr. Salami
I need help with this maximum and minimum word problem. I appreciate your time.

A man has 70lbs of honey from his honey crop, which can be sold for 40 cents a pound today. Each day he waits the amount of the honey increases by 5 lbs but the price will decrease 2 cents a lb. How many days should he wait to make a maximum profit?

Answer
Hi Roba,
Starting from the present day, we find the revenue function. Suppose he waits for x days, the honey would have increased by 5x lbs and the price would have decreased by 2x cents a lb.
The revenue function is therefore
R(x) = (70 + 5x)(40 - 2x)
    = 2800 - 140x + 200x - 10x^2
    = 2800 + 60x - 10x^2
The number of days x that maximizes revenue is found when the derivative of R(x), i.e dR/dx, is equal to zero.
dR/dx = 60 - 20x
equating to zero,
60 - 20x = 0
20x = 60
x = 3
And so he needs to wait for 3 days to maximize revenue.

I hope it helps.

Regards