Solve the Problem $p$ Of a Certain Product and the Quantity Sold

question 173

Essay

Solve the problem.
-The price $p$ of a certain product and the quantity sold $x$ obey the demand equation $p = - \frac { 2 } { 3 } x + 200,0 \leq x \leq 300$ .
Suppose that the cost $C$ of producing $x$ units is $C = \frac { \sqrt { x } } { 20 } + 800$ . Assuming that all items produced are sold, find the cost $C$ as a function of the price $p$ .

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Definitions:

Output

Refers to the quantity of products or services produced by a business, industry, or economy.

Marginal Cost

The increase in total cost that arises from an increase in production by one additional unit.

Average Variable Cost

The total variable cost of production divided by the quantity of output produced, representing the average cost of each unit of output when only variable costs are considered.

Cost-Minimizing Firm

A business entity that seeks to achieve production at the lowest possible cost.