Chapter 5 Flashcards
What does a production function indicate?
how much output is produced by input
input=independent variable=argument
What factors determine production?
employees, machinery, land ownership, raw materials
What is z in a function?
z= dependent variable
it is the assigned variable for a function with 2 variables or a pair of numbers (x,y)
z=f(x,y)
What is an intersection curve (intersections)?
A section through a 3D space for functions with two independent variables
Vertical intersection (x or y plane)
Horizontal intersection (z plane)
z=f(x,y)
What do the variables of a production function represent?
X=employees
Y= machines
Z=output
What is a contour line?
Horizontal intersection in the z plane. It indicates the different combinations of employees and machines for a certain output
What is a partial derivative?
When one independent variable is assumed to be a constant
What is the derivative of ln (u)?
Uā/U
What is a direct second order partial derivative?
fxx and fyy
What is a mixed second order partial derivative
fxy and fyy
When is optimization used in math?
To determine extreme points (min/max) in multivariable functions
What must be considered in optimization problems?
The constraint
When do you have a max during optimization?
fxx (x0,y0) <0 ,fyy (x0,y0) <0 and fxx(x0,y0) *fyy (x0,y0) > fxy (x0,y0)^2
When do you have a min during optimization?
fxx (x0,y0)>0 ,fyy (x0,y0) >0 and fxx(x0,y0) *fyy (x0,y0) > fxy (x0,y0)^2
How do you find critical point in optimization?
fx (x0,y0)=0
fy (x0,y0)=0
When do you have a saddle point?
fx=fy=0
And
fxx*fyy<fxy^2
When to use system of equations?
When you have 2 equations with 2 unknowns
In business, what do you look for to maximize in optimization?
When you look for max profit, production level, benefits
In business, what do you look for to minimize in optimization?
Minimal costs
What are restrictions called in business math?
Constraints
What are the formulas to find max and min in optimization with constraints?
max f(x,y) subject to g(x,y)=c
min f(x,y) subject to g(x,y)=c
C is real number
