# Linear Programming Models

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Overview and Rationale

This assignment is designed to provide the students with hands-on experiences utilizing the Excel Solver to optimize profits or costs via linear programming models in real-life applications. You are provided with a business scenario and you are asked to create a model to optimize profits and costs.

Course Outcomes

This assignment is directly linked to the following key learning outcomes from the course syllabus:

• Use descriptive, Heuristic and prescriptive analysis to drive business strategies and actions
• Incorporate general industry practices in end-to-end analytics development cycles, including data management, data engineering, analytics modeling, optimization, and strategic development

Assignment Summary

## A Profit and Cost Model

A northern hardware company is studying a plan to open a new distribution center in southeast. The company plans to rent a warehouse and an adjacent office, and distribute its main products to the local dealers. The company has decided to initially start with four of its main products: Pressure washers, Go karts, Generators, and Water pumps. The table below describes how much each of the products will cost the company (including transportation costs):

Item Cost (in Dollars)

Pressure Washer 350

Go-kart 365

Generator 400

Case of 5 Water Pumps 650

The company has set aside a purchasing monthly budget of \$190,000 for the new location. The selling prices (per unit) for each item are given in the table below:

Item Cost (in Dollars)

Pressure Washer 489.99

Go-kart 699.99

Generator 689.99

Case of 5 Water Pumps 799.99

Other than the budget, another of the company’s concern is the available space in the warehouse. The warehouse has 92 shelves and each shelf is 30 ft long and 6 ft wide. Pressure washers and generators each are stored on 6 ft by 6 ft pallets whereas each Go Kart is stored on an 8 ft by 5 ft pallet. Furthermore, a 6 ft by 6 ft pallet is used to store four cases of water pumps

For promoting its brand products, the company’s marketing department has decided to allocate at least 25% of its inventory to pressure washers and Go Karts, and sell at least twice as many generators as water pumps.

As a consultant, your task is perform a monthly analysis using a linear programming model to maximize the company’s net profit. As a guide, consider the following:

1. In a Word document, write the mathematical formulation of the problem.
2. Set up the linear programming formulation in an Excel workbook.
3. Use the Excel Solver to solve the problem, and generate a Solver sensitivity report.
4. Describe the optimal solutions obtained in the Word document. These will consist of the inventory level for all four products and the optimal monthly profit.
5. One of the decision variables has an optimal value of zero. Use the Solver sensitivity report to determine the smallest selling price for that item so that this optimal zero solution value changes to a non-zero value.
6. In the word document explain whether, in addition to the \$190,000 allocated to the purchasing budget during the first month, the company should allocate additional money. If yes, calculate the amount of additional investment do you recommend, and how much should the company expect its net monthly profit to increase as a consequence of this increase?
7. In the word document, explain whether you recommend that the company should rent a smaller or a larger warehouse. In any case, indicate the ideal size of your recommended warehouse in square feet, and indicate how much this change in the size of the warehouse will contribute to the monthly profit.

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