Week 2

Question 1

How do you model that x is less than 0.75 of the total

Answer 1

x/(x+y) <= 0.75

or x < (0.75*(x+y))

Question 2

How do you know if a function is a linear program

Answer 2

whne all the constrains and objective function can be modelled with a line

Question 3

Whenever you have a changing variable/decision variable that is squared or cubed or…. or square rooted

Answer 3

it is a NON LINEAR program

Question 4

Can you divide by a decision variable

Answer 4

NO!

Question 5

Is (x/(x+y)) Linear or not?

Answer 5

NON LINEAR

but… you can make it like this:

x < (0.75*(x+y))

Question 6

3 elements of linearity

Answer 6

Additivity
Proportionality
Divisible

Question 7

What makes an LP Linear?

Question 8

The shaded area where all constraints are satisifeid

Answer 8

feasible region

Question 9

What is the objective?

Answer 9

The function you want to maximize!! Z=x+y

BASICALLY you draw this on the plane and push it outwards!!! until you hit a corner point

Question 10

If the function is non linear, then how do you solve?

Answer 10

Well.. its challenging because you need to do calc to find the optimal point

Question 11

Types of LP: Allocation
Covering
Set covering
Blending
Aggregate Planning
Network

Answer 11

distributing a resource (usually maxing profit)

minimizing a cost, but there is a cosntraint

each member of set 1 must be covered by set 2

Blending: may be maxing or mining, some sort of proportion requirement added to the constraint

agg:

nw:

Question 12

Set Covering

Answer 12

MAKE THE TABLE!!!!

Question 13

SolverSolve true= NO DIALOG
Solver Solve False= Dialog

Question 14

3 features of linearity

Answer 14

ADDITIVITY: contribution from one decision gets added/subtracted from other decisions

PROPORTIONALITY: contribution of any given decision grows in proportion to value of corresponding decision variable

DIVISIBLE: a fraction decision variable is meaninful

Question 15

If your objective is non linear

Answer 15

Then it is hard to find an optimal point along the curve!

Question 16

What if your constraints were not linear

Answer 16

once again hard to find optimal point along curve

Question 17

6 LPS

Answer 17

allocation

covering

set covering

blending

aggregate planning

network

Question 18

Allocation

Answer 18

maxing profit based on resource constriants

RESOURCES ARE NOT DV! THE ALLOCATION IS DV

Question 19

Covering

Answer 19

mining an objective (Cost) subject to benefit constraints on required coverage

Question 20

Set Covering

Answer 20

member of agiven set must be covered by acceptable member of another set

Question 21

Blending

Answer 21

may be maxing/mining prob with twist of some proporation requiriments to constraints

Question 22

Agg planning

Answer 22

determmine workforce levels and prod levels for multiperiod time horizon

e.g. determining hiring of new employees

Question 23

Network

Answer 23

product people or funds flow throuhg a netowkr of nodes connceted by arcs

Question 24

In solver sensitivity, waht does allowable increase and decrease man?

Answer 24

it means that you can change the coefficients by x amount without changing the optial solution

Question 25

Shadow price

Answer 25

how much you are willing to pay for 1 more unit of whateveere line you are looking at? and then this changes your profit by the amount of the shadow price

Question 26

What is a binding constraint

Answer 26

A constraint that is maed out!

Question 27

when shadow price is 0

Answer 27

it means you are not willing to pay for an extra unit of the constraint

Question 28

when shadow price is non-zero

Answer 28

typically you are willing to pay extra cuz the constraint is binding

Question 29

when do you use automatic scaling?

Answer 29

only when small number x very large number