A farmer estimates that if he harvests his soybean crop now, he will obtain 1,00

Question

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 that the price will drop at a rate of 50 cents per bushel per week. In addition, it is likely he will experience spoilage of approximately 200 bushels per week for each week he delays harvesting. When should he harvest his crop to maximize revenues and how much revenue will he earn at that time? Note that partial weeks are allowed.

Explanation / Answer

Now harvest =1000 @3.00 = 3000

Delay by t weeks = (1000+1200t-200)(2.50)

= 2000+3000t

Both revenues are equal if

3000= 2000+3000t

Or t = 1/3

As partial weeks are not allowed t=1

When t=1, revenue = 2000+3000 = 5000

Since this is more than 3000 he can wait for one week.

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