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CalculusQ&A LibraryOwners 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.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.

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 – 2*p*.

The revenue is obtained as follows:

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:

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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