SOLUTION: If a farmer digs his potatoes today, he will have 100 bags worth $2 a bag. Every week he waits the crop increases by 10 bags and the price drops by 10 cents a bag. When should the

Question 551695: If a farmer digs his potatoes today, he will have 100 bags worth $2 a bag. Every week he waits the crop increases by 10 bags and the price drops by 10 cents a bag. When should the farmer dig his potatoes in order to maximize his profit?
I appreciate any help:)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If a farmer digs his potatoes today, he will have 100 bags worth $2 a bag.
Every week he waits the crop increases by 10 bags and the price drops by 10 cents a bag.
When should the farmer dig his potatoes in order to maximize his profit?
:
Let w = no. of weeks for max spuds (today, w=0)
:
Profit = no. of bags * price per bag
P = (100 + 10w)(2.00 - .10w)
FOIL
P = 200 - 10w + 20w - w^2
a quadratic equation
f(w) = -w^2 + 10w + 200
max profit occurs at the axis of symmetry, x = -b/(2a); b=10, a=-1
w =
w = +5 weeks will yield max profit (which would be: 150 * 1.50 = $225)

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