Solver Part 1: Table, Chair, Profit Totals

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In this assignment, the goal is to determine the optimal combination of manufacturing tables and chairs that maximizes profit, using Solver in a spreadsheet environment. The setup involves analyzing resource constraints, costs, and minimum production requirements for both products. The process begins with reviewing an initial setup in a spreadsheet, which includes detailed material costs, fabrication times, and profit calculations for each item. Then, the task involves using Solver to identify the production volumes that yield the highest profit while respecting constraints such as minimum production levels and resource limits. Further steps include running sensitivity and limits reports to interpret the effects of changes, adjusting constraints to simulate management decisions, and analyzing how these impact optimal production quantities. Additionally, the assignment includes creating a new spreadsheet for a logistics optimization problem involving two trucks with different cost structures, aiming to minimize total cost over a specified distance, subject to repair cost caps and other constraints. The comprehensive exercise combines linear programming, resource management, and cost minimization techniques through Solver to inform decision-making in manufacturing and logistics scenarios.

Paper For Above instruction

Optimization problems are fundamental in operations management and production planning, often addressed through linear programming techniques implemented via software tools like Excel Solver. This assignment demonstrates the practical application of Solver to determine the most profitable production mix of tables and chairs, considering resource constraints and minimum production requirements. Additionally, it explores logistics cost minimization, showcasing Solver’s versatility in handling diverse business scenarios.

Analyzing the Manufacturing Scenario Using Solver

The primary scenario involves a furniture manufacturer producing tables and chairs. The challenge is to establish the optimal number of each product to maximize profit while adhering to constraints on material availability, fabrication time, and minimum production levels. Each product incurs specific costs based on raw materials (metal tubing, plastic sheets), and fabrication time, with associated costs per unit. The profit per unit is calculated by subtracting these costs from the selling price, which is fixed at $129 for tables and $35 for chairs.

The problem is modeled with decision variables representing the number of tables and chairs to produce. Constraints are integrated to ensure minimum production levels (at least 4 tables and 10 chairs), as well as resource limits on material usage and fabrication time. Solver is configured to maximize total profit, which is the sum of individual profits from each product, considering the production quantities.

Reviewing the Solver setup involves analyzing the target cell (total profit), the changing cells (production volumes), and the constraints (minimum production, resource limitations). Running Solver yields the optimal production quantities, which should be assessed through sensitivity and limits reports. The sensitivity report reveals how much the objective function's coefficients can vary before the current solution becomes suboptimal, providing insights into the stability of the solution. The limits report details the permissible range for the constraint bounds, indicating which resource limits or minimum requirements are binding or could be relaxed or tightened without changing the optimal solution.

Impact of Adjusting Constraints: Scenarios and Solutions

One scenario involves increasing fabrication capacity from 480 minutes to 600 minutes and raising the minimum number of chairs to 16. Running Solver with these parameters determines the new optimal production plan. Typically, additional capacity allows for higher production volumes, potentially increasing total profit, while a higher minimum chair production requirement might shift the balance between products. The result should be detailed with the corresponding number of tables and chairs, and the total profit calculated accordingly.

Another scenario considers production line delays for tables, increasing fabrication time to 26 minutes per unit, but reducing fabrication time for chairs to 3 minutes. With original production minimums, Solver can be re-run to evaluate the new optimal production mix. Likely outcomes include a shift toward producing fewer tables and more chairs to maximize profit within the constrained resource availability. The solution details should specify the optimal quantities and total profit, reflecting adjustments due to operational constraints.

Logistics Cost Minimization Using Solver

The second part involves a logistic problem where two trucks—a new and an old one—are used for a contract spanning 90,000 miles. Each truck has unique cost structures, including fuel, payments, driver wages, repairs, and miscellaneous costs. The objective is to allocate miles between the trucks to minimize total costs while respecting constraints such as a repair cost cap of $14,000.

Setting up this problem involves creating a decision variable for the number of miles assigned to each truck, calculating total costs based on per-mile costs, and ensuring that total miles sum to 90,000. The repair cost constraint must also be incorporated. Solver is configured to minimize total costs, and the optimal division of miles provides the most cost-effective way to fulfill the contractual requirement.

Running Solver yields the distribution of miles for each truck, which should be interpreted alongside cost details and the repair cap. The resulting solution informs fleet management decisions, balancing operational costs and reliability considerations while adhering to constraints.

Conclusion

Through these scenarios, the application of Solver exemplifies decision-making in manufacturing and logistics. Utilizing linear programming models, companies can optimize resource utilization, maximize profits, and minimize costs. The analyses demonstrate the importance of understanding constraints, sensitivity, and the impact of operational adjustments. Mastery of Solver enhances strategic planning and operational efficiency, supporting data-driven business decisions.

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