Imagine that you have a set of weights to use with a scale. You have three 1-pound weights, three 5-pound weights, and two 25-pound weights. (a) Using different combinations of these weights, is it possible to produce all numbers 1–50 on the scale? If not, which numbers are you unable to produce? (b) What combination of 1-pound, 5-pound, or 25-pound weights would you need to add to your collection to be able to represent all weights in the range 1–50?