# [SOLVED] revenue word problem...

• Mar 4th 2008, 01:40 PM
omgconfusion
[SOLVED] revenue word problem...
ok, so i've been trying to solve this problem for a friend (he's in a lower level college math course). now, i'm by no means great at math, but i'm fairly competent at it. however, this problem is a you know what:

The manager of a peach orchard is trying to decide when to arrange for picking the peaches. If they are picked now, the average yield per tree will be 100 pounds, which can be sold for .40 cents per pound. Past experience shows that the yield per tree will increase about 5 pounds per week, while the price will decrease about .2 cents per pound per week.
a) let x represent the number of weeks that the manager should wait. find the income per pound
b) find the number of pounds per tree
c) find the total revenue from a tree

i feel so stupid :\$
i guess this is what happens when you don't take a math course for 1 year+.
any help would be extreeeeeeeemely appreciated.

edit: equation should come out to be a parabolic function
• Mar 4th 2008, 05:11 PM
roy_zhang
First I am not sure whether you mean 0.40 cents/pound and 0.2 cents/pound, please double check the number in your post. I am assuming you mean 40 cents/pound and 2 cents/pound

OK, here we go.

Let $x$ represent the number of weeks that the manager should wait in order to maximize his revenue;

Let $R(x)$ be the total revenue in cents after x weeks from one tree;

According to the description, we have:
$R(x) = (100+5x)(40-2x)=-10x^2+4000$

The graph of the revenue function is a parabola, which opens down. It implies that when $x=0$, $R(x)$ achieves its maximum, which is $R(x)=4000$ cents (40 dollars).

Hence,
(a) Income per pound will be $40-(0)(2)=40$ cents.

(b) Number of pounds per tree will be $100+(0)(5)=100$ pounds.

(c) Total revenue is 4000 cents (40 dollars) (it is the maximum you can get).