Solving an equation for all possible integer solutions

Problem: A person spends 15 dollars at the store. Eggs cost 1 dollar. Milk costs 2 dollars and bread costs 3 dollars.

I'm attempting to create a list of all possible integer solutions to the problem. I attempted to solve the problem with the solve function

Solve[e 1 + m 2 + b 3 == 15 && e > = 0 && m >= 0 && b >= 0, {e, m, b}, Integers]

I'm not solving this exact problem. In theory its the same thing except a lot bigger. The above code works and produces an answer, but I get stuck in the larger calculation. Should I go about solving the problem another way? If so how?

Comments

plotting - Plot 4D data with color as 4th dimension

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plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1....

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