Please Help with Steps

Question

A company producing steel construction bars uses the function C(x)=0.02x2. -3.4x+150 to model the unit in dollars for producing x bars. For what number of bars is the cost at a minimum? What is the cost at that level of production?

Answer 1

C(x) represents the Cost, and x represents the number of bars (i.e. C(x) represents your y values on a graph, and x is x). You will note because the leading coefficient is a positive number, the graph opens up (parabola). Therefore, you will be looking at the vertex as a minimum.

You will use the x vertex formula (since the quadratic was given to you in standard format).

1. X(vertex) = -b/(2a)
2. x = 3.4/(2*.02)
3. x = 85 this is the number of bars produced for minimum cost.
4. C(x) = .02(85)² -3.4(85) + 150 will yield the cost at that level
5. C(x) = $5.50

Make sense on the process?

Answer 2

C(x)=.02x^2 -3.4x + 150. take the derivative and set equal to zero

C'(x) = .04x -3.4 =0, solve for x

x =3.4/.04 = 340/4 = 85 is the cost minimizing output level

C(85) = .02(85)^2 -3.4(85) +150 = 7225/50 - 289+150 = 144.5 -139 = $5.50

C(85) = $5.50 = minimum cost when output = 85