A Manufacturer Finds That the Revenue Generated by Selling X $R ( x ) = 40 x - 0.2 x ^ { 2 }$

question 60

Essay

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function, $R ( x ) = 40 x - 0.2 x ^ { 2 }$ where the revenue $R ( x )$
is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

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Definitions:

Materials Price Variance

Materials price variance is the difference between the actual cost of materials used in production and the expected (or standard) cost, indicating efficient materials purchasing.

AQ × AP

Represents the multiplication of the Actual Quantity (AQ) by the Actual Price (AP), often used in financial and operational analyses.

Total Variance

The overall difference between planned or standard costs and the actual costs incurred.

Total Labor Variance

The difference between the actual cost of labor and the budgeted or standard cost of labor over a period.