An Iron Monger can weigh goods up to 40lb in 1lb increments by cutting a 40-inch iron bar into specific lengths. The optimal method involves making two orthogonal cuts, resulting in weights of 1lb, 2lb, 4lb, 8lb, 16lb, and 9lb, allowing for the measurement of any weight from 1 to 40lb. Various cutting strategies were discussed, including using powers of 2 and 3 to achieve the desired weights. The discussion highlighted the importance of allowing weights on both sides of the scale for optimal measurement. Ultimately, the most efficient solution requires six cuts to achieve the necessary weights without waste.