Week 17

Question 1

When is Langragian method not suitable?

Answer 1

if the optimal solution is an interior point where the constraint is not binding

Question 2

Annual rate of interest?

Answer 2

P(1+r)^t where t is years

Question 3

Quarterly rate of interest?

Answer 3

P(1+r/4)^4t where t is years

Question 4

Continual rate of interest?

Answer 4

Pe^rt where t is years

Question 5

What does lamda in lagrangian tell us?

Answer 5

If increase in first variable (not equality) by change in t

then new variable thing will be original cost x lambda x epsolon

or if increase in equality

original amount (not equality) + lambda + epselon

Question 6

Monthly rate of interest?

Answer 6

P(1+r/m)^mt

Question 7

re (effective annual rate)?

Answer 7

P(1+re) = Pe^r
= P(1+r/m)^m

Question 8

Present discounted value eq?

Answer 8

P = S /(1+r/m)^mt
or S/e^rt

Question 9

AP?

Answer 9

a+(n-1)d

Question 10

Sum of AP?

Answer 10

n/2(2a+(n-1)d)

Question 11

GP? un

Answer 11

un = ar^n-1

Question 12

Sum of GP?

Answer 12

a (1-r^n)/1-r

Question 13

Way to show convex and concave function using principle minors?

Answer 13

all prinicple minors are positive for matrix with just numbers (convex)

odd is negative even is positive (concave)