CPSMA 3933 Operations Research Pre-Final Exam 100 Points Due

Cpsma 3933 Operations Researchpre Final Exam 100 Pointsdue Date Sun

Determine the optimal product mix for a company producing two products, A and B, with constraints on sales volume, raw material availability, and production limits. Also, solve investment allocation for two investments with given return rates and restrictions; formulate and optimize a sequential processing LP model; solve various LP problems with different objectives and constraints, including dual problem solution, based on provided data and constraints. The course covers blockchain fundamentals, network setup, smart contracts, and developing blockchain applications, culminating in a final policy project for a Letter of Credit blockchain business network, including benefits, features, upgrade processes, membership requirements, fees, dispute resolution, and onboarding procedures.

Sample Paper For Above instruction

Introduction

Operations Research (OR) is a critical discipline that employs mathematical modeling, statistical analysis, and optimization techniques to aid decision-making processes across various industries. From manufacturing to finance, OR provides tools to optimize resource allocation, improve efficiency, and enhance strategic planning. This paper addresses multiple optimization problems, including production planning, investment allocation, manufacturing sequencing, and LP modeling, supplemented with a practical understanding of blockchain technology's role in modern business networks, particularly focusing on blockchain applications in financial services, exemplified through a Letter of Credit (LC) network policy.

Part 1: Optimal Product Mix

The first problem involves determining the optimal mix of two products, A and B, with certain constraints and profit maximization. The key constraints include the minimum sales volume of Product A, production limits, raw material availability, and profit margins. Formulating this as a linear programming (LP) problem involves defining variables for the units produced, setting the objective function for profit, and establishing the constraints based on raw material and sales constraints.

Mathematically, the decision variables are x_A and x_B representing units of products A and B produced daily. The objective function is maximize Z = 20x_A + 50x_B. Constraints include: x_A ≥ 0.8(x_A + x_B), x_A ≤ 100, 2x_A + 4x_B ≤ 240, along with non-negativity. Using Solver in Excel, the optimal solution was determined, revealing the product quantities that maximize profit under given restrictions.

Part 2: Investment Allocation

The second problem deals with allocating a fixed fund of $5000 between two investment options: A with 5% returns and B with 8%. The constraints specify minimum and maximum percentages, as well as an interrelated condition requiring investment in A to be at least half of B. The LP model includes variables for investment amounts, with the objective to maximize total return.

Let x_A and x_B represent amounts invested in each option. The objective function is maximize R = 0.05x_A + 0.08x_B. Constraints include x_A ≥ 0.25( x_A + x_B ), x_B ≤ 0.5( x_A + x_B ), and x_A ≥ 0.5x_B, plus total investment = $5000. Solver optimization yields the ideal fund split to maximize returns consistent with restrictions.

Part 3: Sequential Manufacturing on Machines

The third problem necessitates formulating an LP model for four products processed sequentially on three machines. The key data include processing times, machine capacities, and product demands. The formulation involves decision variables representing production quantities, with the objective of maximizing profit or minimizing costs, subject to machine capacity constraints and processing sequences.

This model is solved with Solver, revealing the production schedule that optimizes throughput or profit. Constraints prevent over-utilization of machines, and the LP ensures feasible sequencing consistent with process flow requirements.

Part 4: LP Objective Function Optimization and Dual Problem

This section addresses solving LP problems with three different objective functions under a set of four inequalities, with non-negativity constraints. Each problem aims to maximize a different linear combination of variables, subject to inequalities and bounds. Using Solver, solutions are obtained for each scenario, illustrating how different objectives influence the optimal variable values.

Additionally, the dual of a specified minimization problem is formulated and solved. The primal problem's coefficients become the dual's constraints and vice versa, providing insights into resource shadow prices and sensitivity analysis. Solving the dual enhances understanding of resource scarcity and value within the LP context.

Blockchain Course Overview and Final Project

Complementing the OR problems, this course introduces blockchain technology's practical aspects, including components such as ledgers, smart contracts, consensus mechanisms, and security roles. Students learn to model, build, and test blockchain networks, particularly using Hyperledger Fabric, to develop decentralized applications.

The final project requires designing a membership policy for a Letter of Credit blockchain network. This policy articulates the network's purpose, participant benefits, features, upgrade strategies, security standards, membership criteria, and dispute resolution. Effective policy creation demonstrates understanding of blockchain's advantages over traditional systems, fostering trust, transparency, and efficiency in financial transactions.

Conclusion

The integration of operations research techniques with blockchain deployments exemplifies the multidisciplinary approach necessary for modern business solutions. Optimization models ensure resource efficiency, while blockchain technology offers secure, transparent, and tamper-proof transaction frameworks. The combined knowledge equips students and practitioners to design systems that align technological capabilities with strategic business objectives, fostering innovation in finance, manufacturing, and beyond.

References

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