Question

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

Answer 1

To get minimized number of x steel bars, we differentiate the equation and then equate to zero:
d/dx (C(x) = 0.02x² – 3.4x + 150)
C'(x) = 0.02(2)x – 3.4 = 0

Solving for x
0.04x – 3.4 = 0
x = 85 steel bars

For minimum cost,
C(x = 85) = 0.02(85)² – 3.4(85) + 150 = 5.5 dollars