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When no more than 110 units are produced, the cost of producing y units is given by C(x).
C(x) = 0.2x^3 – 24x^2 + 1514x +30,064
How many units should be produced in order to have the lowest possible average cost?
___ units should be produced. (Round to one decimal place as needed.)​

Respuesta :

raphealnwobi

Producing 73.8 units gives the lowest possible average cost.

The average cost (AC) is the ratio of the total cost to the number of units produced. It is given by:

AC = C(x) / x

AC = (0.2x³ – 24x² + 1514x +30064) / x

AC = 0.2x² - 24x + 1514 + 30064/x

The lowest possible average cost is at AC' = 0. Hence differentiating the average cost, gives:

AC' = 0.4x - 24 - 30064/x²

0.4x - 24 - 30064/x² = 0

0.4x³ - 24x² - 30064 = 0

Solving the cubic polynomial gives:

x = 73.8 units

Therefore the lowest possible average cost is when 73.8 units are produced.

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