# LP question

• Jan 21st 2010, 08:23 AM
Danneedshelp
LP question
I have a simple question about solving LP problems using the graphical method.

Ex:

Let $\displaystyle x_{1}$=number of units of special risk insurance
$\displaystyle x_{2}$=number of units of mortgages

Maximize:

$\displaystyle 5x_{1}+2x_{2}=Z$

Where the coefficients are $5 per unit of special risk insurance and$2 per unit mortgages.

Subject to:

$\displaystyle 3x_{1}+2x_{2}\leq{2400}$

$\displaystyle x_{2}\leq{800}$

$\displaystyle 2x_{1} \leq{1200}$

and $\displaystyle x_{1}>0, x_{2}>0$

Where the coefficients on the LHS are in "work-hours per unit" and on the RHS the numbers represent "work-hours available".

Q: Simply, is it alright if I re-write the RHS of the constraint system in hundreds of hours so I can scale down my graph without changing the LHS of the equations into hundreds of hours?

I have had a few HW problem where the LHS consists of small fractional numbers and the RHS is made up of large numbers and it makes using the graphical method of solving kind of awkward, because the graident of objective function is usually relatively small. Should I just scale up my graident vector instead of changing the rest of my graph?

So, basically, can I scale down one side of the equation without scaling down the other?
• Jan 21st 2010, 09:38 AM
CaptainBlack
Quote:

Originally Posted by Danneedshelp
I have a simple question about solving LP problems using the graphical method.

Ex:

Let $\displaystyle x_{1}$=number of units of special risk insurance
$\displaystyle x_{2}$=number of units of mortgages

Maximize:

$\displaystyle 5x_{1}+2x_{2}=Z$

Where the coefficients are $5 per unit of special risk insurance and$2 per unit mortgages.

Subject to:

$\displaystyle 3x_{1}+2x_{2}\leq{2400}$

$\displaystyle x_{2}\leq{800}$

$\displaystyle 2x_{1} \leq{1200}$

and $\displaystyle x_{1}>0, x_{2}>0$

Where the coefficients on the LHS are in "work-hours per unit" and on the RHS the numbers represent "work-hours available".

Q: Simply, is it alright if I re-write the RHS of the constraint system in hundreds of hours so I can scale down my graph without changing the LHS of the equations into hundreds of hours?

I have had a few HW problem where the LHS consists of small fractional numbers and the RHS is made up of large numbers and it makes using the graphical method of solving kind of awkward, because the graident of objective function is usually relatively small. Should I just scale up my graident vector instead of changing the rest of my graph?

So, basically, can I scale down one side of the equation without scaling down the other?

No, and there is no need to, the scales on both axes should go from 0 to about 1000.

CB
• Jan 21st 2010, 10:38 AM
Danneedshelp
Quote:

Originally Posted by CaptainBlack
No, and there is no need to, the scales on both axes should go from 0 to about 1000.

CB

So, the graident vector (5,3) is going to be very small, but that doesnt matter, since I only need it for finding the direction of the max value; Correct?

Sorry for my elementary questions, I just cannot understand my teacher (or his notes) and don't have a textbook yet.