Producing Widgets: Revenue and Profit maximization
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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?
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Solution Summary
This solution analyzes the revenue and profit maximization for a company producing widgets.
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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 - ...
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