Chapter 4

Question 1

what is the other name for local max/min?

Answer 1

relative max/min

Question 2

What is the other name for global max/min?

Answer 2

absolute max/min

Question 3

What is the difference between global maximum vs local maximum

Answer 3

global is the overall maximum
and local is where the function reaches it’s peak

Question 4

How do you know if you are dealing with a maximum or minimum?

Answer 4

when f’(x) = 0
the tangent is horizontal

Question 5

How do we know if it’s a local maximum?

Answer 5

f”(x) <0

Question 6

How do we know if it’s a local minimum?

Answer 6

f”(x) > 0

Question 7

How do you know if it’s a global maximum?

Answer 7

f” (x) <0 for all x ∈ D

Question 8

How do you know if it’s a global minimum?

Answer 8

f” (x) >0 for all x ∈ D

Question 9

What is the economic principle?

Answer 9

scarcity of resources forces companies and consumers to make rational decisions

Question 10

What is optimization problems?

Answer 10

When companies and consumers try to maximize profit/benefit and minimize costs they encounter problems

Question 11

What is the minimum principle?

Answer 11

to use the least amount of resources to achieve goal

Question 12

What is the minimization problem

Answer 12

achieving goals by using the least resources can lead to problems (inefficiency, low quality)

Question 13

What is the maximum principle?

Answer 13

to company or consumer wants to obtain highest level of benefit/profit possible

Question 14

What is maximization problem

Answer 14

by doing maximum principle an actor can run into problems (overproduction, saturation)

Question 15

How do you solve optimization problems?

Answer 15

By determining extreme points using differential calculus

Question 16

What is local maximum?

Answer 16

the highest point among function values in the vicinity

Question 17

What is global maximum

Answer 17

The highest point in the entire domain

Question 18

What is a marginal extremum

Answer 18

the maximum or minimum at the edge of the domain

Question 19

What is a corner or peak

Answer 19

a sharp change in a function, creating a non-smooth linear function. cannot be measured using derivatives since slope is undefined

Question 20

How do you know if an extreme point exists

Answer 20

when f’(x) =0
AND
f”(x) < or > than 0

if x∈ D then its global extrema

Question 21

How do you determine a saddle point?

Answer 21

If f’‘(x) =0
If f’’‘(x) is NOT 0 - it’s a saddle point

Question 22

How do you know if it’s an inflection point?

Answer 22

in f’‘(x) =0
AND f’’‘(x) ≠ 0

Question 23

What are the steps for curve sketching

Answer 23

1. Find domain
2. Find 0 in f(x)
3. Determine extreme points with f’(x)
4. Determine points of inflection f”(x)
5. Verify inflection points with f”‘(x)
6. Characterize slope by using number line

Question 24

How do you calculate maximum profit?

Answer 24

MR=MC
Or MR-MC=0

Question 25

What are the variables in a production function?

Answer 25

Y(L) = units of goods produced L= number of employees

Question 26

What can you determine by differentiating the production function?

Answer 26

marginal productivity

Question 27

How do you calculate profit maximization?

Answer 27

1. P=R-C, find P'(x)=0, confirm w/ P"(x) or R'-C'=P' 2. MR=MC, 3. Quadratic function -b/2a

Question 28

What does MR=MC mean in economics? What if it’s not MR=MC?

Answer 28

that's when a business maximizes profit if MR>MC, then producing more increases profit, because additional revenue outweighs additional costs if MR

Question 29

How do you get the revenue function?

Answer 29

through the price function R(x)= p(x)*x

Question 30

What are the factors in a logistics function? e.g. S(x) = 40024+ 0.98x/10 000+200/x

Answer 30

The logistics function shows the different costs to optimize order quantity 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

Question 31

What does differentiating the logistics function tell you?

Answer 31

lowest cost possible, how much items one should order

Question 32

What are other names for the economic principle? 2

Answer 32

rational principle economic efficiency principle

Question 33

What are the necessary conditions for an extrema?

Answer 33

Slope = 0 f’(x) = 0

Question 34

What are the sufficient conditions for an extrema? (to distinguish if min or max)

Answer 34

If f ‘’ (x) < 0 , then max If f ‘ ‘ (x ) > 0 , the min It is global for all x D

Question 35

How does a function look like if it has local/global maximum

Answer 35

Local: function is concave when the slope is zero and only around vicinity Global: the entire function is concave down

Question 36

What are the different costs in logistics? 5

Answer 36

PDHIS Price per item Delivery Handling costs Interest costs for capital tied up in the warehouse Storage costs