Chapter 4 Flashcards
what is the other name for local maximum?
relative maximum
What is the other name for global maximum?
absolute maximum
What is the difference between global maximum vs local maximum
global is the overall maximum
and local is where the function reaches it’s peak
How do you know if you are dealing with a maximum or minimum?
when f’(x) = 0
the tangent is horizontal
How do we know if it’s a local maximum?
f”(x) <0
How do we know if it’s a local minimum?
f”(x) > 0
How do you know if it’s a global maximum?
f” (x) <0 for all x ∈ D
How do you know if it’s a global minimum?
f” (x) >0 for all x ∈ D
What is rational principle or economic efficiency principle?
scarcity of resources forces companies and consumers to make rational decisions
What is optimization problems?
When companies and consumers try to maximize profit/benefit and minimize costs they encounter problems
What is the minimum principle?
to use the least amount of resources to achieve goal
What is the minimization problem
achieving goals by using the least resources can lead to problems (inefficiency, low quality)
What is the maximum principle?
to company or consumer wants to obtain highest level of benefit/profit possible
What is maximization problem
by doing maximum principle an actor can run into problems (overproduction, saturation)
How do you solve optimization problems?
By determining extreme points using differential calculus
What is local maximum?
the highest point among function values in the vicinity
What is global maximum
The highest point in the entire domain
What is a marginal extremum
the maximum or minimum at the edge of the domain
What is a corner or peak
a sharp change in a function, creating a non-smooth linear function. cannot be measured using derivatives since slope is undefined
How do you know if an extreme point exists
when f’(x) =0
AND
f”(x) < or > than 0
if x∈ D then its global extrema
How do you determine a saddle point?
If f’‘(x) =0
check if f’’‘(x) =0 if yes it’s a saddle point
How do you know if it’s an inflection point?
in f’‘(x) =0
AND f’’‘(x) ≠ 0
What are the steps for curve sketching
- Find domain
- Find 0 in f(x)
- Determine extreme points with f’(x)
- Determine points of inflection f”(x)
- Verify inflection points with f”‘(x)
- Characterize slope by using number line
How do you calculate maximum profit?
MR=MC
Or MR-MC-0
What are the variables in a production function?
Y(L) = units of goods produced
L= number of employees
What can you determine by differentiating the production function?
marginal productivity
How do you calculate profit maximization?
- P=R-C, find P’(x)=0, confirm w/ P”(x)
or R’-C’=P’ - MR=MC,
- Quadratic function -b/2a
What does MR=MC mean in economics?
that’s when a business maximizes profit
if MR>MC, then producing more increases profit, because additional revenue outweighs additional costs
if MR<MC, then producing less increases profit, because cost savings exceed lost revenue
How do you get the revenue function?
through the price function
R(x)= p(x)*x
What are the factors in a logistics function?
The logistics function shows the different costs to optimize order quantity
e.g.
S(x) = 40024+ 0.98x/10 000+200/x
S(x)= costs
40024 = fixed costs
0.98x/10000= variable costs per bottle (per 10 000 bottles)
200/x= ordering costs spread over x bottles
What does differentiating the logistics function tell you?
lowest cost possible, how much items one should order
