# Linear Programming: Shares and Dividends

• Mar 9th 2009, 11:58 AM
glaboratory
Linear Programming: Shares and Dividends
Hi all,

I have two eqns which are related to stock and dividends which i think LP could help to solve( .. i hope).

5.5x + 2.5y = theta
67.00x + 28y = 200 000
x>0, y>0, theta>0

I derived the above two eqns from this:
Stock A is @ 67.00
Stock B is @ 28.00

Stock A pays 5.5 dollars per share annually
Stock B pays 2.5 dollars per share annually.
(ie. if i get 1 x 67.00 and 0 x 28.00, that year i'll get $5.50) My question is how to derive the set of {x,y} that would yield a max theta? Million thanks, Gary • Mar 9th 2009, 01:17 PM masters Quote: Originally Posted by glaboratory Hi all, I have two eqns which are related to stock and dividends which i think LP could help to solve( .. i hope). 5.5x + 2.5y = theta ====> "I assume this is your profit function" 67.00x + 28y = 200 000 ====> "I don't understand where this came from" x>0, y>0, theta>0 I derived the above two eqns from this: Stock A is @ 67.00 Stock B is @ 28.00 Stock A pays 5.5 dollars per share annually Stock B pays 2.5 dollars per share annually. (ie. if i get 1 x 67.00 and 0 x 28.00, that year i'll get$5.50)

My question is how to derive the set of {x,y} that would yield a max theta?

Million thanks,
Gary

Hi Gary,

My guess is that the above equation in red should be an inequality to represent some kind of restraint, but there's not enough info to determine what that restraint is.

Do you just have \$200,000 to invest? If so, the restraint would be:

$67x+28y \leq 200000$

But, even with these constraints, we end up with an unbounded region. So, we need more detail.
• Mar 10th 2009, 12:54 AM
glaboratory
Hi masters

Yes, i have 200000 to invest and yes your constraint is correct

if i am correct, i think the unbounded region is the theta.

i think i am not sure how to estimate theta such that x and y are bounded.

Million thanks,
Gary