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Answer :
Final Answer:
The cost of producing 3700 units is $222,375.00. The cost of producing 200 additional units is $9,400.00.
Explanation:
To find the cost of producing a certain number of units, we need to integrate the marginal cost function with respect to the quantity of units produced. The given marginal cost function is C′(x) = 150 - 0.08x + 0.00002x² dollars.
a) To find the cost of producing 3700 units, we integrate the marginal cost function from 0 to 3700:
Cost = ∫(150 - 0.08x + 0.00002x²) dx evaluated from 0 to 3700
Cost = [150x - 0.04[tex]x^2[/tex] + 0.00001x³] evaluated from 0 to 3700
Cost = 222375
Therefore, the cost of producing 3700 units is $222,375.00.
b) To find the cost of producing 200 additional units, we integrate the marginal cost function from 3700 to 3900 (3700 + 200):
Additional Cost = ∫(150 - 0.08x + 0.00002x²) dx evaluated from 3700 to 3900
Additional Cost = [150x - 0.04x² + 0.00001x³] evaluated from 3700 to 3900
Additional Cost = 9400
Hence, the cost of producing 200 additional units is $9,400.00.
In summary, the cost calculations involve integrating the given marginal cost function within specific ranges of units produced to find the total cost and the additional cost for a given production level.
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