Expert: Steve Holleran - 11/26/2007

Question
12000 customers at $16/mo.  Will lose 400 customers for every dollar that rates are increased.  Determine the monthly charge that will maximize their revenue.

Answer
Hi Marlene.

Okay, first, the revenue R at $16/mo is

        R = 12000 * 16 = $192,000.

Let x = the number of $1 increases.   Then you have :

R = (# customers) * (charge per customer)

 = (12,000-400x) * (16 + 1x)

 = 192,000 + 12,000x -6400x -400x^2

  =192,000 + 5600x - 400x^2.

Using x = -b/2a to find the x-value for the vertex of the parabola represented by this equation, we have:

x = -5600/ -800 = 7.  Since the parabola would open downwards because of the -400x^2, this value gives the maximum.

So, R(7) = (12,000 - 2800) * (16 + 7) = $211,600.

So, you want the monthly charge to be $23 per customer.

Hope this helps
Steve