The Quantity Demanded Per Month of an Item Is Related $p = \frac { 45 } { 0.04 x ^ { 2 } + 1 } , \quad 0 \leq x \leq 20$

question 62

Short Answer

The quantity demanded per month of an item is related to the unit price by the demand equation $p = \frac { 45 } { 0.04 x ^ { 2 } + 1 } , \quad 0 \leq x \leq 20$
where $p$ is measured in dollars and $x$ is measured in units of a thousand. How many items must be sold by the manufacturer to maximize its revenue?
Hint: Recall that the revenue is given by $R = p x$ .

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Definitions:

Average Variable Cost Curve

A graphical representation that shows the relationship between a firm's average variable costs and its quantity of output.

Marginal Cost

The cost associated with producing an extra unit of output, crucial for decision-making in production and pricing strategies.

Total Costs

The complete amount of costs incurred by a business to produce a specific amount of goods or services, including fixed and variable costs.

Total Variable Costs

The sum of all costs that vary with the level of output, including costs for raw materials, labor, and other expenses that increase as production increases.