```Question 57392
A company uses the formula C(x) = 0.02x^2 - 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?
:
The x value of the vertex is the number of bars for which the unit cost is at its minimum.
We can find that by:
When a quadratic equation is in standard form:  {{{highlight(ax^2+bx+c)}}}
In what you typed, a=0.02 b=-3.4, and c=150
The x value of the vertex is found by this formula:{{{highlight(x=-b/2a)}}}
{{{x=-(-3.4)/(2(.02))}}}
{{{highlight(x=85)}}}
85 is the number of bars at which the unit cost is at its minimum.
:
The unit cost at that level would be: C(-b/2a)
Just substitute the x-value of the vertex into the C(x) function and solve.
{{{C(85)=0.02(85)^2-3.4(85)+150}}}
{{{C(85)=0.02(7225)-3.4(85)+150}}}
{{{C(85)=144.5-289+150}}}
{{{C(85)=5.5}}}
The unit cost at that level is: C=\$5.50

Check that against what you got.
Happy Calculating!!!```