2-B. A farmer estimates that if he harvests his soybean crop now, he will obtain 1,000 bushels, which he can sell at $3.00 per bushel. However, he estimates that this crop will increase by an additional 1,200 bushels of soybeans for each week he delays harvesting, but the price will drop at a rate of 50 cents per bushel per week; in addition, it is likely that he will experience spoilage of approximately 200 bushels per week for each week he delays harvesting. When should he harvest his crop to obtain the largest net cash return, and how much will be received for his crop at that time

Question

Business

Orion Davidson

25 February, 12:01

2-B. A farmer estimates that if he harvests his soybean crop now, he will obtain 1,000 bushels, which he can sell at $3.00 per bushel. However, he estimates that this crop will increase by an additional 1,200 bushels of soybeans for each week he delays harvesting, but the price will drop at a rate of 50 cents per bushel per week; in addition, it is likely that he will experience spoilage of approximately 200 bushels per week for each week he delays harvesting. When should he harvest his crop to obtain the largest net cash return, and how much will be received for his crop at that time

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Answers (1)

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Jaylyn Jensen · Answer 1

the farmer should wait for two weeks in order to be able to obtain 3,000 bushels and sell then at $2 per bushel, total revenue $6,000

Explanation:

time to harvest bushels price revenue

today 1,000 $3 $3,000

1 week 2,000 $2.50 $5,000

2 weeks 3,000 $2 $6,000

3 weeks 4,000 $1.50 $6,000

4 weeks 5,000 $1 $5,000

5 weeks 6,000 $0.50 $3,000

net increase per week = + 1,200 bushels - 200 bushels = 1,000 bushels