Calculus 3'9

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3.10 Business and Economics Applications
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Summary of Business Terms and Formulas
Basic Terms
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Summary of Business Terms and Formulas
Marginals
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Example 1
A manufacturer determines that the profit derived
from selling x units of a certain item is given
by
a. Find the marginal profit for a production
level of 50 units.
b. Compare this with the actual gain in profit
obtained by increasing the production from 50 to
51 units.
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a. Find the marginal profit for a production
level of 50 units.
The marginal profit is given by
When x 50, the marginal profit is
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b. Compare this with the actual gain in profit
obtained by increasing the production from 50 to
51 units.
For x 50 and 51, the actual profits are
Thus the additional profit obtained by increasing
the production is
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The number of units x that consumers are willing
to purchase at a given price p per unit is
defined as the demand function, p f(x).
Example 2 Finding the Marginal Revenue
La Mesita has determined that the monthly demand
for its flautas is
Find the increase in revenue per flauta (marginal
revenue) for monthly sales of 20,000 flautas.
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Find the increase in revenue per flauta (marginal
revenue) for monthly sales of 20,000 flautas.
Total revenue is given by R xp, we have
and the marginal revenue is
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Find the increase in revenue per flauta (marginal
revenue) for monthly sales of 20,000 flautas.
When x 20,000, the marginal revenue is
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Example 3 Finding the Maximum Profit
In marketing a certain item, a business has
discovered that the demand for the item is
represented by
The cost of producing x items is given by
Find the price per unit that yields a maximum
profit.
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Example 3 Finding the Maximum Profit
Find the price per unit that yields a maximum
profit.
Profit Revenue Cost
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Example 3 Finding the Maximum Profit
Find the price per unit that yields a maximum
profit.
Profit Revenue Cost
The maximum profit occurs when the price is 1.00.