M119 Notes, Lecture 15
Review (time permitting)
Ex. Find all local extrema and inflection points for f ( x) x 4 x 2 5
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
Ex. The demand for a product is p 40 0.05q . Find the quantity that maximizes
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:
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