Question 150353
Minimizing cost. A company uses the formula C(x) = 0.02x² - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?
.
Simply by looking at a quadratic equation we can tell whether opens up or down.  If it opens down -- the vertex gives you the maximum.  If it opens up -- the vertex gives you a minimum.
To do this, consider the general quadratic form:
y = ax^2 + bx + c
You simply need to look at the coefficient of the x^2 term (a) -- if it is positive, it opens up.  if it is negative, it opens down.
.
Looking at:
C(x) = 0.02x² - 3.4x + 150 
the value of 'a' is 0.02 (positive) therefore, the vertex will be a "minimum".
.
The x coordinate of the vertex can be found with:
x = -b/2a
x = -(-3.4)/2(.02)
x = (3.4)/(.04)
x = 85
.
For what number of bars is the unit cost at its minimum? 85 stabilizer bars 
.
C(x) = 0.02x² - 3.4x + 150 
C(85) = 0.02(85)² - 3.4(85) + 150 
C(85) = 144.5 - 289 + 150 
C(85) = 5.5
.
What is the unit cost at that level of production? $5.50