If w pounds per acre of nitrogen fertilizer are spread on a corn field the yield
ID: 2859398 • Letter: I
Question
If w pounds per acre of nitrogen fertilizer are spread on a corn field the yield is
210(3800/w+24)
bushels of corn per acre. Corn sells for $4.75 per per bushel and fertilizer costs $0.65 per pound. All other costs of growing and harvesting the corn total $450 per acre, and don't depend on the amount of fertilizer used.
A) How much nitrogen fertilizer per acre should the farmer use to maximize his net dollar return per acre?
_____lb/acre
B) If the farmer uses the optimum amount of fertilizer what will be his net dollar return per acre?
________$ per acre.
Explanation / Answer
net profit = fixed cost +variable cost -revenue
profit = 450 + 0.65 *w - (210-3800/(w+24))
profit = 240 +0.65w +3800/(w+24)
dP/dw = 0.65 -3800/(w+24)^2 = 0
3000 = 0.65*(w+24)^2 . solving we have
w= 43.94 lb/acre ------ANSWER A
net profit = 240+0.65*43.94 +3800/(43.94+24)
net profit = $324.49 ------ANSWER B