Linear Programming Case Study
Your instructor will assign a linear programming project for this assignment according to the following specifications.
It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.
You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.
Writeup.
Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.
After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.
Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.
Excel.
As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.
Your work will be graded according to the following rubric.
Points: 110 | Assignment 1: Linear Programming Case Study | ||||
Criteria | Unacceptable Below 60% F | Meets Minimum Expectations 60-69% D | Fair 70-79% C | Proficient 80-89% B | Exemplary 90-100% A |
Explain what type of problem this is and the approach you are taking (20%) | Did not explain what type of problem this is and the approach taken, or did so insufficiently. | Insufficiently explained what type of problem this is and the approach taken | Partially explained what type of problem this is and the approach taken | Satisfactorily explained what type of problem this is and the approach taken | Thoroughly explained what type of problem this is and the approach taken |
Objective function specified correctly in writeup (10%) | Objective function is specified incorrectly, with both coefficients incorrect or missing. | Objective function is specified, but one (1) coefficient is incorrect. | Coefficients for objective function are correct, but whether this is a max or min problem is incorrect. | Objective function is specified correctly. | |
Constraints are specified correctly in writeup (10%) | Constraints are specified incorrectly or missing. | Some constraints are correctly specified. | Most constraints are correctly specified. | All constraints are correctly specified, buy applicable nonnegativity constraints are omitted. | All constraints are correctly specified, including nonnegativity constraints, if applicable. |
Specified L.P. Model is correctly translated to Excel (10%) | Specified L.P. Model is incorrectly translated into Excel | Specified model is translated to Excel in a partially correct manner | Specified model is translated to Excel in a mostly correct manner | Specified model is correctly translated to Excel | |
Correct Answer is Obtained (10%) | Correct optimum is not obtained | Correct optimum is obtained | |||
Correctly answer the sensitivity analysis part of the problem. (15%) | Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness | Insufficiently explained and/or provided a partially correct answer to the sensitivity analysis part of the problem | Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem | Satisfactorily explained and correctly answered the sensitivity analysis part of the problem | Thoroughly explained and correctly answered the sensitivity analysis part of the problem |
Correctly answer the shadow price part of the problem. (15%) | Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness | Insufficiently explained and/or provided a partially correct answer to the sensitivity analysis part of the problem | Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem | Satisfactorily explained and correctly answered the sensitivity analysis part of the problem | Thoroughly explained and correctly answered the sensitivity analysis part of the problem |
5. Writing / Grammar and mechanics (10%) | Serious and persistent errors in grammar, spelling, and punctuation. | Numerous errors in grammar, spelling, and punctuation. | Partially free of errors in grammar, spelling, and punctuation. | Mostly free of errors in grammar, spelling, and punctuation. | Free of errors in grammar, spelling, and punctuation. |