# Find linear combinations that meet certain criteria

Hey,

I am quite new to SAGE, this is my first project. I'm not even sure if it is solvable or not, but here is what I want to do:

• w_1 is the smallest multiple of 5 that is >= (volume / 30)
• w_n = w_1 + 5*n
• w_max is the largest multiple of 5 that is <= ((volume / 24) + 30)
• were n increases until w_n == w_max

I want to find all solutions to:

• (w_1)(r_1) + (w_2)(r_2) + ... + (w_n)*(r_n) == volume

Given each/any r can be any integer from 5 to 10 and that the sum of all r's is less than or equal 30. Volume is just some constant integer multiple of 5 between 5425 and 7200. Its just an initial condition I want to be able to change. Is this possible or is it too many possibilities for SAGE to handle? I have some programing experience (C and .net ) and a little math experience(Calc 1,2 and 3 as well as differential equations) but I don't know were to start really. If there is any more information I can provide that would be useful I would be very happy to do so. I don't expect someone to make it for me, but I'm not quite sure what kind of approach I should be trying use, so I don't really know what to look up. Any help or advice is welcome.

Thanks.

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