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 represent the number of weeks that the manager should wait in order to maximize his revenue;
Let be the total revenue in cents after x weeks from one tree;
According to the description, we have:
The graph of the revenue function is a parabola, which opens down. It implies that when , achieves its maximum, which is cents (40 dollars).
(a) Income per pound will be cents.
(b) Number of pounds per tree will be pounds.
(c) Total revenue is 4000 cents (40 dollars) (it is the maximum you can get).