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A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If X machines are made, then the unit cost is given by the function C(x) = 0.4x^2 - 216x + 36,222 . What is the minimum unit cost?

Respuesta :

Ashraf82

The minimum unit cost of the copy machine is $7,062

Step-by-step explanation:

To find the minimum or maximum value of a function f(x) = y

  • Find f'(x)
  • Equate f'(x) by 0 and find the value of x
  • Substitute the value of x in f(x) to find the minimum or maximum value of f(x)

∵ C(x) represents the unit cost of x machines

∵ C(x) = 0.4 x² - 216 x + 36,222

- To find the minimum unit cost differentiate C(x)

- Remember the differentiation of  [tex]ax^{n}[/tex] is [tex]a(n)x^{n-1}[/tex]

∴ C'(x) = 0.4(2) x - 216(1)

∴ C'(x) = 0.8 x - 216

- Equate C'(x) by zero to find x

∵ 0.8 x - 216 = 0

- Add 216 to both sides

∴ 0.8 x = 216

- Divide both sides by 0.8

∴ x = 270

Substitute x in C(x) by 270 to find the minimum unit cost

∵ C(270) = 0.4(270)² - 216(270) + 36,222

∴ C(270) = 29,160 - 58,320 + 36,222

∴ C(270) = 7062

∴ The minimum unit cost is $7,062

The minimum unit cost of the copy machine is $7,062

Learn more:

You can learn more about differentiation in brainly.com/question/4279146

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