# Thread: optimization problem with no function

1. ## optimization problem with no function

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!

2. ## 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.

3. ## 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?

4. ## 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?

5. ## Re: optimization problem with no function

Yes, so how many km will she travel in second class?

6. ## Re: optimization problem with no function

it would be 1500-1050=450 I think

7. ## Re: optimization problem with no function

Yes, that's correct.