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Answer :
By analyzing the given information and calculating the income for different rates, we determined that the maximum income the rental agency can obtain is 240 per day when they charge a rate of 24 per day and rent out 10 trailers.
To determine the maximum income the rental agency can obtain, we need to find the rate that maximizes the income.
Let's start by analyzing the given information. We know that the agency rents 12 trailers per day at a rate of 16 per day. Additionally, for every 4 increase in the rate, one fewer trailer is rented.
To find the optimal rate, we can create a table and calculate the income for different rates.
Rate | Number of Trailers Rented | Income per Day
[tex]-------------------------------------------------\\16 | 12 | $192\\$20 | 11 | $220\\$24 | 10 | $240\\$28 | 9 | $252\\[/tex]
From the table, we observe that as the rate increases, the number of trailers rented decreases. However, the income per day also increases as the rate per trailer increases.
The income, we need to find the rate that gives the highest income. In this case, the highest income is obtained when 10 trailers are rented, corresponding to a rate of 24 per day. At this rate, the agency earns 240 per day.
The maximum income the rental agency can obtain is 240 per day when they charge a rate of 24 per day and rent out 10 trailers.
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