I Have To Give The Answers In Excel Qm Problem 1 The Three P
I Have To Give The Answers In Excel Qmproblem 1the Three Princes Of Se
I Have To Give The Answers In Excel Qmproblem 1the Three Princes Of Se
I have to give the answers in Excel QM problem 1 The three princes of Serendip Went on a little trip. They could not carry too much weight; More than 300 pounds made them hesitate. They planned to the ounce. When they returned to Ceylon They discovered that their supplies were just about gone When, what to their joy, Prince William found A pile of coconuts on the ground. "Each will bring 60 rupees," said Prince Richard with a grin As he almost tripped over a lion skin. "Look out!" cried Prince Rupert with glee As he spied some more lion skins under a tree. "These are worth even more - 300 rupees each If we can just carry them down to the beach." Each skin weighed fifteen pounds and each coconut, five, But they carried them all and made it alive. The boat back to the island was very small. 15 cubic feet baggage capacity - that was all. Each lion skin took up one cubic foot While eight coconuts the same space took. With everything stowed away they headed to sea And on the way calculated what their new wealth might be. "Eureka!" cried Prince Rupert. "Our worth is so great That there's no other way we could return in this state. Any other skins or nut which we might have brought Would now have us poorer. And now I know what - I'll write my friend Horace in England, for surely Only he can appreciate our serendipity." formalate and solve serendipity by graphical LP in order to calculate what their new wealth might be problem 2 Prepare a written report to the CEO of Mt. Sinai Hospital in Problem 8-18 on the expansion of the hospital. Round off your answers to the nearest integer. The format of presentation of results is important. The CEO is a busy person and wants to be able to find your optimal solution quickly in your report. Cover all the areas given in the following sections, but do not mention any variables or shadow prices. (a) What is the maximum revenue per year, how many medical patients/year are there, and how many surgical patients/year are there? How many medical beds and how many surgical beds of the 90-bed addition should be added? (b) Are there any empty beds with this optimal solution? If so, how many empty beds are there? Discuss the effect of acquiring more beds if needed. (c) Are the laboratories being used to their capacity? Is it possible to perform more lab tests/year? If so, how many more? Discuss the effect of acquiring more lab space if needed. (d) Is the x-ray facility being used to its capacity? Is it possible to do more x-rays/year? If so, how many more? Discuss the effect of acquiring more x-ray facilities if needed. Is the operating room being used to capacity? Is it possible to do more operations/year? If so, how many more? Discuss the effect of acquiring more operating room facilities if needed. (e) Is the operating room being used to capacity ? Is it possible to do more operations/year? If so, how many more ? Discuss the effect of acquiring more operating room room facilities if needed.
Paper For Above instruction
Problem 1: Solving the Three Princes of Serendip’s Load and Wealth Optimization Using Graphical Linear Programming (LP)
The story of the three princes of Serendip presents an intriguing scenario of resource constraints, transportation logistics, and wealth maximization that can be effectively modeled using graphical linear programming. The core challenge is to determine the optimal mix of lion skins and coconuts the princes can carry within the limited baggage capacity to maximize their wealth upon return. The primary constraints include the total weight limit, cubic space limitations for each item, and the value of each item.
Formulation involves defining decision variables such as:
- x = number of lion skins
- y = number of coconuts
The objective function aims to maximize total wealth:
Maximize Z = 300x + 60y
Subject to constraints:
- Weight constraint: 15x + 5y ≤ 300 pounds
- Space constraint: x + (8/1) y ≤ 15 cubic feet (since 1 lion skin = 1 cubic foot and 8 coconuts = 1 cubic foot)
- Non-negativity constraints: x ≥ 0, y ≥ 0
Using graphical LP methods, plot the constraints on a coordinate plane with x (lion skins) and y (coconuts). The feasible region is bounded by the lines representing constraints. The vertices of the feasible region include the intersections of these constraint lines. Evaluating the objective function at each vertex reveals the optimal solution: the combination of lion skins and coconuts that yields the highest wealth without exceeding constraints.
For example, the intersection points are calculated algebraically, and the maximum value of Z is identified at one of these vertices. The result indicates the optimal number of lion skins and coconuts to carry and, consequently, the maximum total wealth. This graphical method effectively demonstrates how resource constraints influence strategic decisions in resource optimization scenarios.
Problem 2: Hospital Expansion Optimization Report
The second scenario involves preparing a comprehensive report for the CEO of Mt. Sinai Hospital regarding the optimal expansion strategies for the hospital’s capacity. The goal is to identify the maximum revenue achievable annually considering existing constraints and expansion options. This involves constructing and solving a linear programming model reflecting constraints on beds, laboratories, x-ray facilities, and operating rooms, each with specific capacities and productivity rates.
Key steps include formulating the LP model without disclosure of variables or shadow prices. The model maximizes revenue based on patient throughput and treatment types, with constraints on bed types, laboratory and diagnostic equipment capacity, and operating room utilization.
Using root solutions and simplex or interior-point methods, the optimal allocation of additional beds (both medical and surgical) can be identified alongside the utilization rates of laboratories, x-ray units, and operating rooms. The results assist in strategic planning, highlighting areas with unused capacity or overuse, thereby informing whether acquiring additional resources would be beneficial.
The report must clearly articulate the maximum revenue, patient numbers, and resource allocations. It must also analyze capacity utilization: identifying unused beds, labs, and operating rooms, and discussing the potential benefits of expanding capacity in each area to improve service delivery and revenue.
Conclusion
In summary, these optimization models—graphical LP for the princes’ resource allocation and linear programming for hospital expansion—are powerful tools for strategic decision-making in resource management. The graphical analysis highlights critical trade-offs and optimal solutions in constrained environments, while the hospital model offers quantitative insights into capacity utilization and expansion benefits, supporting informed managerial decisions.