Question
Asked Apr 26, 2019
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Owners of a boat rental company that charges customers between $95 and $475 per day have determined that the number of boats rented per day n can be modeled by the linear function n(p)=950−2p, where p is the daily rental charge. How much should the company charge each customer per day to maximize revenue? Do not include units or a dollar sign in your answer.
 
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Expert Answer

Step 1

Given information:

Given that p is the daily rental charge and n(p) be the number of boats rented per day.

The number of boats rented per day is modelled by the linear function n(p) = 950 – 2p.

The revenue is obtained as follows:

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Step 2

Obtain the daily rental rate at which the revenue will be maximum.

The objective is to find the value of p at which the revenue R(p) will be maximum.

The value of p at which R’(p) = 0 and R’’(p) < 0 maximizes the revenue.

The daily rental rate at which the revenue will be maximum is obtained as 237.5 from the calculation given below:

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Step 3

Check whether R’’(p) < 0 at p = 237.5:

If R’’(p) < 0 at p = 237.5 then p = 237.5 is the daily rental...

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