A 300-room hotel in Las Vegas is filled to capacity every night at $80 a room....

A 300-room hotel in Las Vegas is filled to capacity every night at $80 a room. For each $1 increase in rent, 3 fewer rooms are rented.

At what rate should the rooms be rented to produce the maximum revenue and how many rooms are rented at that rate? What is the maximum revenue? Write your results in a sentence as what each number means and represents. Please include all steps needed

Expert Solution

To find maximum revenue we have to find revenue in terms of single variable and then have to use following procedure

For relative maximum or minimum

To maximize or minimize a function f(x) 1st we need to find its critical points

For critical points we need to put differentiation of f(x) equal to zero i.e. f '(x) = 0

Then check second derivative of f(x) i.e. f ''(x) is positive or negative at critical numbers If f ''(x) >0 then that gives minimum value of f(x) and if f ''(x) <0 then that give maximum value of f(x)

milcah answered 2 years ago

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