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?

Question

Mathematics

Mariela Clarke

19 February, 04:06

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?

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Answers (1)

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Valerie Downs · 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