This assignment presents a linear programming (LP) model designed to maximize the profits of Specific Motors, a manufacturer of three car models (X, Y, and Z). The model considers net revenues, labor hours, and steel constraints. The solution includes the formulation of an objective function and constraints, followed by an optimal solution obtained using a spreadsheet optimizer, where the optimal production levels for each model are determined. The analysis further explores the concept of shadow prices, particularly in relation to labor hours and steel. It evaluates the potential addition of a new car model (Model Q) to the production plan, using shadow prices to assess its impact on profitability and concludes that Model Q should not be considered. The assignment demonstrates the practical application of LP in production planning and resource allocation, providing insights into optimization and constraint analysis.
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