Reference no: EM133125290

Question: A hardware company is studying a plan to open a new distribution center in the southeast. The company plans to rent a warehouse and an adjacent office, and distribute its main products to local dealers. The company has decided to initially start with four of its main products: pressure washers, gokarts, generators, and water pumps. Management has set aside a monthly budget of $170,000 for purchasing. Other than the budget, the available space in the warehouse is another concern. The warehouse has 82 shelves and each shelf is 30 feet long and 5 feet wide. Each pressure washer and each generator is stored on a 5 foot by 5 foot pallet, each go-kart is stored on an 8 foot by 5 foot pallet, and four cases of water pumps (with five water pumps in each case) are stored on a 5 foot by 5 foot pallet. Also, for promoting its brand products, the company has decided to allocate at least 30% of its inventory to pressure washers and go-karts, and keep at least twice as many generators as water pumps. Determine the number of items of each type that should be sent to the distribution center to maximize the company's monthly profit.

a) One of the decision variables has an optimal value of zero. Explain what the selling price of that item should be for this optimal solution value to change.

b) Explain whether the company should set aside additional budget money beyond the $170,000 allocated to the merchandise during the first month. If yes, how much do you recommend, and how much should the company expect its monthly profit to increase as a result?

c) Explain whether you recommend that the company should rent a smaller or a larger warehouse. In any case, indicate the size of yourrecommended warehouse in square feet, and determine how much this change will contribute to the monthly profit.

Specifically, attend to the following critical elements:

I. Scenario Analysis and Model Creation:

a) Introduction: Provide a summary of your selected scenario, highlighting the important aspects that need to be considered and problems that need to be addressed to develop an appropriate model.

b) Mathematical Formula: Create the mathematical formula that will address the problem. Be sure your model aligns to the considerations you highlighted in your introduction and the information that was provided in the scenario.

c) Formula Justification: Explain how you developed this formula. Provide your reasoning for the decisions made, including support when relevant.

II. Model Optimization:

a) Optimization: Optimize the linear objective function by performing iterations of the simplex method. Be sure to illustrate your work in the
appendix of your report.

b) Interpretation: Interpret the results. In other words, now that you have optimized your linear objective function, explain what this means within the context of the problem.

c) Verification: Apply duality theory and interpret the results. Do the results verify your previous results? If not, what do your results show?

III. Sensitivity Analysis:

a) Sensitivity Analysis: Perform a sensitivity analysis on the primal model (the model from I.B) and interpret the results.

b) Process: Illustrate the process both graphically and algebraically. Be sure to provide your work in the appendix of your report so that others can check the accuracy of, and replicate, the process taken.

c) Interpretation: Interpret the results of the sensitivity analysis. How does this affect the optimal solution? What does this tell you about the behavior of your model?

IV. Communication: Through your report, be sure that you are communicating in a manner that can be understood by individuals with varying levels of mathematical understanding. Often when partnering with various organizations, you will interact with individuals who may need more or less technical explanations. Your report will be reviewed for the following:

a) Detail and Importance: When explaining your results, be sure to detail the greater implications of your results within the context of the problem you chose to work on, and the context of operations research in general. You will want to emphasize the greater importance and implications foryour audiences.

b) Varied Methods: When explaining mathematical concepts, be sure to use a variety of methods (textual, graphical, etc.) to communicate your points so that those who read the report will grasp the essential concepts and information.

c) Articulation of Response: In crafting your report, take care to correctly cite external sources of information, organize your report in a logical way, and avoid spelling and grammar inconsistencies and errors.