High School

The marginal cost of producing x tablet computers is C′(x)=150−0.08x+0.00002x2 dollars. What is the cost of producing 3700 units if the setup cost is $80000 ? (Use decimal notation. Give your answer to two decimal places.) cost: 5 If production is set at 3700 units, what is the cost of producing 200 additional units? (Use decimal notation. Give your answer to two decimal places.) additional cost: 5

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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