Marginal cost A division of Ditton Industries manufactures...

Marginal cost A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is $$ C(x)=0.0002 x^{3}-0.06 x^{2}+120 x+5000 $$ where $x$ stands for the number of units produced. a. What is the actual cost incurred in manufacturing the 101 st oven? The 201 st oven? The 301 st oven? b. What is the marginal cost when $x=100,200,$ and $300 ?$

Marginal cost A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these microwave ovens is
$$
C(x)=0.0002 x^{3}-0.06 x^{2}+120 x+5000
$$
where $x$ stands for the number of units produced.
a. What is the actual cost incurred in manufacturing the 101 st oven? The 201 st oven? The 301 st oven?
b. What is the marginal cost when $x=100,200,$ and $300 ?$

Key Concepts

Cost Function

A cost function is a mathematical expression that represents the total cost of production as a function of the number of units produced. It typically includes both fixed costs, which do not change with production level, and variable costs, which do. This function is foundational in analyzing how changes in production volume impact total expenses.

Marginal Cost

Marginal cost refers to the additional cost incurred from producing one extra unit of a product. In economic and mathematical analysis, it is commonly approximated by the derivative of the cost function with respect to the production quantity. This concept is central to deciding optimal production levels and understanding cost efficiency.

Derivative in Calculus

A derivative measures the rate at which a function is changing at any given point. In the context of cost functions, the derivative represents the marginal cost, allowing us to approximate the cost for producing one more unit. This calculus concept is vital for performing marginal analysis in production and economics.

Difference Method for Incremental Cost

The difference method involves calculating the actual cost of producing a specific unit by finding the difference between the total cost at that production level and the total cost at the previous level. This approach provides the actual incremental cost, serving as a practical check against the marginal cost obtained via differentiation.

Transcript

Please give Ace some feedback