Problem 1: A villager estimates that if he picks his orange crop now, he will obtain 2000 boxes of apples, which he can sell at $5 per box. However, he thinks his crop will increase by 150 boxes of apples for each week he delays picking, but that the price will drop at a rate of $0.25 per box per week; in addition, he estimates approximately 30 boxes per week will spoil for each week he delays picking. When should he pick his crop to obtain the largest total cash return? How much will he receive for his crop at that time?

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter10: Systems Of Equations And Inequalities
Section10.FOM: Focus On Modeling: Linear Programming
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Problem 1:
A villager estimates thatif he picks his orange crop now, he will obtain 2000 boxes of
apples, which he can sell at $5 per box. However, he thinks his crop will increase by 150
boxes of apples for each week he delays picking, but that the price will drop at a rate of
$0.25per box per week; in addition, he estimates approximately 30 boxes per week will
spoil for each week he delays picking, When should he pick his crop to obtain the largest
total cash return? How much will he receive for his crop at that time?
Transcribed Image Text:Problem 1: A villager estimates thatif he picks his orange crop now, he will obtain 2000 boxes of apples, which he can sell at $5 per box. However, he thinks his crop will increase by 150 boxes of apples for each week he delays picking, but that the price will drop at a rate of $0.25per box per week; in addition, he estimates approximately 30 boxes per week will spoil for each week he delays picking, When should he pick his crop to obtain the largest total cash return? How much will he receive for his crop at that time?
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