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Sergeeva-Olga [200]
2 years ago
15

The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dol

lars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
Mathematics
1 answer:
Licemer1 [7]2 years ago
5 0

9514 1404 393

Answer:

  $562,500 per hour

Step-by-step explanation:

The cost will be a minimum where C'(x) = 0.

 C'(x) = 0.56x -0.7 = 0

  x = 0.7/0.56 = 1.25

The cost at that production point is ...

  C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625

The minimum production cost is $562,500 per hour for production of 1250 items per hour.

_____

<em>Additional comment</em>

This is different than the minimum cost <em>per item</em>. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.

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