The independent variable is the variable that:
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The revenue function is,
For maximum and minimum value, the first derivative of function is equal to 0.
Determine the first derivative of revenue function.
For maximum and minimum value, R'(x) = 0. So
Since x = 700 corresponds to maximum or minimum value of revenue.
Determine the second derivative of revenue function.
Since second derivative of revenue function is less than 0 for every value of x. So x = 700 corresponds to maximum value of revenue.
So 700 villas rented to produce maximum revenue.
Answer: 700 villas