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If the cost function for a commodity is

C(x) = 1/90 ₓ₃ + ₂ₓ₂ + 2x + 18 dollars
find the marginal cost MC at x = 3 units. (Round your answer to two decimal places.) MC =
Tell what the marginal cost predicts about the cost of producing 1 additional unit. The cost of producing 1 additional unit is
Tell what the marginal cost predicts about the cost of producing 2 additional units. The cost of producing 2 additional units is

User Glxce
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1 Answer

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Final answer:

The marginal cost (MC) at x = 3 units is $26.20. The cost of producing 1 additional unit is $26.20. The cost of producing 2 additional units is $52.40.

Step-by-step explanation:

The cost function for a commodity is given by C(x) = (1/90)x^3 + 2x^2 + 2x + 18 dollars. To find the marginal cost (MC) at x = 3 units, we need to calculate the derivative of the cost function with respect to x. Taking the derivative of C(x) with respect to x gives: C'(x) = (1/30)x^2 + 4x + 2. Substituting x = 3 into the derivative, we have: C'(3) = (1/30)(3)^2 + 4(3) + 2 = 9/10 + 12 + 2 = 26.20 dollars (rounded to two decimal places).

The marginal cost (MC) at x = 3 units is $26.20.

The marginal cost predicts the additional cost of producing 1 additional unit. So, the cost of producing 1 additional unit is equal to the marginal cost. Therefore, the cost of producing 1 additional unit is $26.20.

Similarly, the marginal cost predicts the additional cost of producing 2 additional units. So, the cost of producing 2 additional units is equal to twice the marginal cost. Therefore, the cost of producing 2 additional units is 2 * $26.20 = $52.40.

User Shaun Han
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