Marginal cost Suppose that the dollar cost of producing x...

Marginal cost Suppose that the dollar cost of producing $x$ washing machines is $c(x)=2000+100 x-0.1 x^{2} .$ a. Find the average cost per machine of producing the first 100 washing machines. b. Find the marginal cost when 100 washing machines are produced. c. Show that the marginal cost when 100 washing machines are produced is approximately the cost of producing one more washing machine after the first 100 have been made, by calculating the latter cost directly.

Marginal cost Suppose that the dollar cost of producing $x$
washing machines is $c(x)=2000+100 x-0.1 x^{2} .$
a. Find the average cost per machine of producing the first 100
washing machines.
b. Find the marginal cost when 100 washing machines are
produced.
c. Show that the marginal cost when 100 washing machines
are produced is approximately the cost of producing one
more washing machine after the first 100 have been made, by
calculating the latter cost directly.

Key Concepts

Average Cost

Average cost is determined by dividing the total cost by the number of units produced. It provides a per-unit cost measure that is useful for assessing efficiency and pricing decisions. In production analysis, calculating the average cost helps in understanding how costs are distributed across each unit produced.

Marginal Cost

Marginal cost is the increase in total cost that arises from producing one additional unit of output. It is computed as the derivative of the cost function with respect to the number of units. This concept is crucial in decision-making as it shows the cost impact of a small change in production level, often used to optimize resource allocation.

Cost Function

A cost function represents the total cost of producing a given number of items. It typically includes fixed costs plus variable costs that depend on the level of production. In problems like this, the cost function models how the cost changes as production increases, serving as a basis for further analyses such as calculating average and marginal costs.

Differentiation in Cost Analysis

Differentiation is employed in cost analysis to derive marginal cost from a cost function. By taking the derivative, one calculates the rate at which cost changes with respect to production. This approach approximates the additional cost incurred by producing one more unit and demonstrates the relationship between calculus and economic decision-making.

Transcript

Please give Ace some feedback