Problem Set

Quadratic Function


HIDE SOLUTION

 

1. The publisher of an medical newsletter estimates that with x thousand subscribers its monthly revenue and cost (in thousands of dollars) are given by the following:

 

            R(X)  = 32x - .21x2

 

            C(x)  =  195  + 12x

 

Determine the number of subscribers needed for the publisher to break-even.

 

Solution:

 

Profit equals revenue less cost. The breakeven point occurs where profit is zero or when  revenue equals cost.

 

            Profit = R(x)  - C(x)

 

           

           

            set profit  = 0

 

           

 

Solve using the quadratic formula where a = 195, b = 20, and c = .21.

 

         

 

 

 

                  

 

Breakeven points occur where the publisher  has either 12,000 or 84,000 subscribers. Between these two points the publisher will be profitable.

 

 

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