Calculating how many set lengths go into a variable length

Hi everyone,

I'm currently trying to calculate how many standard lengths or a combination of standard lengths go into lengths of variable length. But I'm unable to find any solutions as other optimisation solutions require me to input how many times I want my standardised components to fit inside.

At work our components are in sets of

73mm, 75mm, and 77mm

Or

110m, 115mm

and these fit into aluminium tracks of varying length.

These components are acceptable if they have a combined length of a bit more than the given aluminium track, however having the combined length shorter than the track is unacceptable. This is due to the parts pertaining to window blinds, where full coverage is needed without light leaking from behind. These pieces can overlap inside the track.

E.g. Using components of 73mm, 75mm, and 77mm, how can they best fit to make a length of 2682mm?

If someone is able to guide or help me make a spreadsheet where I can input varying lengths and see how many components of each length I need to fully cover.

Don't know if a small solver model could be of use but I've set up one. The green cells is your input, the gray cells are solver results. The cell E4 is used to set a more
even distribution of the different lengths.

You can play around a bit with this number and see how that changes the number of different length to make up your target length.

Alf