Problema Solution

Suppose C(x)=x2−8x+24 represents the costs, in hundreds, to produce x thousand pens. How many pens should be produced to minimize the cost? What is the minimum cost?

Answer provided by our tutors

The problem statement is ambiguous, but we assume that "x2" is intended to be "x^2" (x-squared).  Such an equation is a quadratic expression and solving for a minimum point would be the minimum cost. 

 

The expression "x^2-8x+24" factors by graphing "y=x^2-8x+24" to:

factor through graphing

y=(x-4)^2 + 8

 

The minimum cost is when x=4, when 4 pens are produced, the cost is the minimum.