Discuss, in a detailed paragraph, the rationale behind using traditional costing versus activity-based costing (ABC) in modern manufacturing environments, using Ford Motors as a case study. Highlight the limitations of traditional costing in accurately assigning overhead costs to products compared to the more nuanced approach of ABC. Calculate the overhead allocation for Ford's Mustang and F-150 models, assuming Mustang incurs $80,000 and F-150 incurs $120,000 in overhead costs. Illustrate the allocation process under both costing methods.