Variables In Air Conditioners And Fans To Produce 40-60 Obje

variablesair Condfansunits To Produce4060objective Function

The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each involves specific wiring and drilling times. Each air conditioner requires 3 hours of wiring and 2 hours of drilling, while each fan requires 2 hours of wiring and 1 hour of drilling. The available time for wiring is 240 hours, and for drilling, up to 140 hours can be utilized. The profit per unit for air conditioners is $25, and for fans, it is $15. The goal is to determine the optimal number of units of each product to produce to maximize profit, adhering to the constraints of available wiring and drilling hours. Using Excel's Solver, this linear programming problem will be solved to find the quantities that maximize total profit while satisfying the resource limitations.

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Optimizing production to maximize profit is a fundamental objective in manufacturing operations, requiring rigorous analysis of resource constraints and product profitability. The given case of The Electrocomp Corporation exemplifies a typical linear programming problem where the goal is to determine the optimal quantities of two products—air conditioners and large fans—that maximize profit within the bounds of available resources.

Firstly, defining decision variables is essential. Let x denote the number of air conditioners to produce, and y denote the number of large fans. The objective function aims to maximize total profit, calculated as 25x + 15y, where the coefficients represent profit per unit of each product.

Constraints arise from resource limitations. The wiring and drilling hours impose the most significant restrictions. The wiring constraint is represented as 3x + 2y ≤ 240, reflecting that the combined wiring hours required for both products cannot exceed the total available wiring hours. Similarly, the drilling constraint is 2x + y ≤ 140, limiting the total drilling hours used. Since production cannot be negative, non-negativity constraints x ≥ 0 and y ≥ 0 are also included.

Using Microsoft Excel's Solver, these constraints and the objective function can be input into a linear programming model. Solver's optimization algorithm will then identify the values of x and y that maximize profit without violating resource limitations. The resulting solution will specify the optimal production quantities, providing strategic guidance for manufacturing scheduling.

The solution process involves setting up the decision variables in Excel cells, defining the objective cell as the sum of profit contributions, and adding the constraints regarding wiring and drilling hours. Upon running Solver, the optimal values will be obtained, indicating how many units of each product to produce for maximum profit.

This case highlights the importance of linear programming in manufacturing decision-making, as it allows managers to allocate resources efficiently and improve profitability. The ability to model constraints and objectives mathematically assures data-driven decisions, minimizing waste and maximizing returns.

Furthermore, integrating sensitivity analysis enables understanding the robustness of the optimal production plan. For this case, exploring how changes in profit margins or resource availability impact the solution can be valuable for strategic adjustments in production policies.

In conclusion, the application of linear programming through tools like Excel Solver provides a systematic approach for solving complex production problems. For The Electrocomp Corporation, this method facilitates optimal resource utilization, guides production scheduling, and enhances overall profitability, demonstrating the critical role of operations research in manufacturing management.

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