The manager of a peach orchard is trying to decide when to arrange for picking t
ID: 2855270 • Letter: T
Question
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 80 cents per pound. Past experience shows that the yield per tree will increase about 5 pounds per week, while the price will decrease about 4 cents per pound per week.
a.) Let x represent the number of weeks that the manager should wait. Find the total revenue from a tree.
b.) When should the peaches be picked in order to produce maximum revenue?
c.) What is the maximum revenue?
Explanation / Answer
a)Let x represent the number of weeks that the manager should wait
yeild per tree =100+5x pounds
price per pound =80 -4x cents
total revenue from tree R=yeild per tree*price per pound
total revenue from tree R=(100+5x)(80 -4x)
total revenue from tree R=8000-20x2
B) FOR MAXIMUM REVENUE dR/dx =0
=>0 -40x =0
=>x=0
peaches should be picked immediately in order to produce maximum revenue
c)maximum revenue =8000-20*02
maximum revenue =8000cents
maximum revenue =80$
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