# Producing Widgets: Revenue and Profit maximization

Scenario:

A company produces q widgets per day where q can be treated as a continuous variable. They can be sold for a price P(q) where P(q) = P0 * max {(1 - q/q0), 0}

Questions:

A. What quantity maximizes the manufacturer's revenue?

B. If manufacturing costs increase linearly with the number of widgets made (cost: C(q) = c * q), what quantity will maximize the manufacturer's profit?

https://brainmass.com/business/sales-revenue/producing-widgets-revenue-profit-maximization-538832

#### Solution Preview

Part A

Revenue: R(q) = Price * Quantity

Maximum revenue occurs when R(q) is maximum and q < q0

If q > q0 the revenue will be zero

Revenue = R(q) = P(q) * q = P0 * (1 - ...

#### Solution Summary

This solution analyzes the revenue and profit maximization for a company producing widgets.

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