# optimization problem with no function

• Nov 4th 2012, 08:55 PM
kingsolomonsgrave
optimization problem with no function
Attachment 25549

This problem seems to be an optimization problem but I don't know how to tackle it since it gives no functions.

Thanks for any help!
• Nov 4th 2012, 09:04 PM
MarkFL
Re: optimization problem with no function
This doesn't appear to me to be an optimization problem. You are given information to write 2 linear equations in 2 variables.
• Nov 4th 2012, 09:24 PM
amillionwinters
Re: optimization problem with no function
I agree, this is not an optimization problem. EDIT: Well, I guess you could consider the task to be optimizing the distance Agatha can travel first class.

I'll get you started, though:

Let $A =$ distance, in km, traveled first class.
Let $B =$ distance, in km, traveled second class.

$.40A + .10B = 465$

$A + B = 1500$

Now, how can you relate these two equations to each other?
• Nov 4th 2012, 09:39 PM
kingsolomonsgrave
Re: optimization problem with no function
$0.4x+0.1y=465$ and $x+y=1500$ then i solved for y in the first equation and got $y=4650-4x$ which I then plugged in to the second forumla and solved for x=1050, which, I think, is the number of kilometers the traveller would ride first class, is that right?
• Nov 4th 2012, 09:43 PM
MarkFL
Re: optimization problem with no function
Yes, so how many km will she travel in second class?
• Nov 5th 2012, 06:18 PM
kingsolomonsgrave
Re: optimization problem with no function
it would be 1500-1050=450 I think
• Nov 5th 2012, 06:21 PM
MarkFL
Re: optimization problem with no function
Yes, that's correct.