M119 Notes, Lecture 2

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					                            M119 Notes, Lecture 15

Review (time permitting)
                                                               1     9
Ex. Find all local extrema and inflection points for f ( x)   x 4  x 2  5
                                                               4     2
4.4 Profit, Cost, and Revenue
       We know that a breakeven point can occur when:



       While we can maximize profit when:




Now that we have formulas, we can do this algebraically as well:
Ex. (4) C (q)  q 3  60 q 2  1400 q  1000 for 0  q  50 and the product sells for $788
per unit. At what production level is profit maximized? What is the (total) profit at this
production level?




Ex. The demand for a product is p  40  0.05q . Find the quantity that maximizes
revenue.
At a price of $53, Tim McGraw can sell out the Verizon Wireless Music Center with a
capacity of 24,000. For each additional 25 cents they charge, 150 fewer people will come
(likewise 150 more people per 25 cents they lower the price).

Find the revenue as a function of price alone. What price maximizes the revenue (round
to the nearest cent)?




4.5 Average cost
        I just want to skim over this section as this is often confused with marginal cost.
Average cost is just (total cost)/(number of items). In contrast, the marginal cost tells
you the cost of producing the next item. The confusing thing is that the units are both:
$/unit.


Average Cost = C(q)/q

Marginal Cost = C’(q)

If C(q) = 3q+12, fill in the following table:
 q                       1          2           3          4                5
 Total Cost
 Average
 Cost
Marginal
Cost

				
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