Linear Programming for Resource Allocation and Profit Maximization in Furniture Production
Hemlata Saxena
*
Department of Mathematics, Career Point University, Kota, Rajasthan, India.
Swapnil Sharma
Department of Mathematics, Career Point University, Kota, Rajasthan, India.
*Author to whom correspondence should be addressed.
Abstract
This case study explores the use of linear programming, specifically the simplex method, to optimize the production process in a furniture manufacturing company. The main objective is to maximize profits by identifying the most effective production mix of items such as dining tables, chairs, sofa sets, dressing tables, shoe racks, and beds, all while adhering to constraints on materials like wood, fabric, paint, sun mica, stuffing, accessories, and labor costs.
The study utilizes Excel Solver to apply linear programming and solve the problem of profit maximization. By formulating the objective function and constraints within Solver, it computes the best possible production quantities for each product, ensuring maximum profitability while staying within resource limits.
The results indicate an optimal solution with the following production quantities: 0 dining tables, 0 chairs, 0 sofa sets, 3.70 dressing tables, 107.40 shoe racks, and 4.81 beds. This production mix yields a maximum profit of ₹2,42,777.78. The findings reveal the optimal number of units to produce for each item, providing valuable insights for businesses on how to efficiently allocate resources and achieve financial targets.
Overall, the case study highlights the power of linear programming, facilitated by Excel Solver, in helping businesses make informed decisions that lead to increased profit margins in environments with limited resources.
Keywords: Linear programming, simplex method, decision variables, optimization, profit maximization, excel