Solve the Problem

question 208

Essay

Solve the problem.
- $$\text { Let } c ( x ) = t \left( p _ { 0 } - p \right) p ^ { 3 } \text { where } t \text { and } p _ { 0 } \text { are constants. Show that } c ( x ) \text { is greatest when } p = \frac { 3 } { 4 } p _ { 0 } \text {. }$$

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Definitions:

Manufacturing Overhead

All manufacturing costs that are not directly associated with the production of a product or service.

Plantwide Predetermined Manufacturing Overhead Rate

A single overhead rate calculated for an entire manufacturing plant, applied to all jobs or products to allocate manufacturing overhead costs.

Machine-Hours

Machine-Hours indicate the total hours that machinery is operating during a specific period of time.

Manufacturing Overhead

All indirect costs associated with the manufacturing process, such as utilities, maintenance, and management salaries.