Question

A farmer has currently 200 crates of apples. And can harvest an additional 10 crates per day. The current price of apples is $120 per crate and is expected to drop $4 each day. When should the farmer sell to maximize his income?

A) On the 7th day.
B) On the 8th day.
C) On the 9th day.
D) On the 10th day.

Answer 1

The farmer should sell his apples on the 7th day to maximize his income.The correct answer is option A.

Step-by-step explanation:

To determine when the farmer should sell his apples to maximize his income, we need to calculate the revenue and costs for each day.

Let's start with the revenue:

• On the 1st day, the farmer can sell 200 crates at $120 per crate, so the total revenue is $24,000.
• On the 2nd day, the farmer can sell 210 crates at $116 per crate (since the price dropped by $4), so the total revenue is $24,360.
• Continuing this pattern, we find that on the 7th day, the total revenue is $24,840.
• On the 8th day, the price would have dropped to $80 per crate and the farmer can sell 220 crates, resulting in a total revenue of $17,600.
• On the 9th day, the total revenue is $17,040.
• On the 10th day, the total revenue is $16,480.

Now, let's calculate the costs:

• On any given day, the farmer incurs no additional costs for harvesting the apples.
• Therefore, the costs remain constant at $0 per day.

To calculate the income, we need to subtract the costs from the revenue. From the calculations, we can see that the income is highest on the 7th day ($24,840), so the farmer should sell his apples on the 7th day to maximize his income.