Project:  

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                         330 

Go-kart                                         370 

Generator                                 410 

(Case of 5 Water Pumps)         635 

Table 1: Costs of products in dollars 

The company has set aside a purchasing monthly budget of $170,000 for the new location. The selling prices (per unit) for each item are given in the table below: 

Item                                 Selling Price (in Dollars) 

Pressure washer                         499.99 

Go-kart                                         729.99 

Generator                                 700.99 

Water pump                                 269.99 

Table 2: Revenues of products in dollars 

Other than the budget, another of the company’s concern is the available space in the warehouse. The warehouse has 82 shelves, and each shelf is 30 ft long and 5 ft wide. Pressure washers and generators each are stored on 5 ft by 5 ft pallets whereas each Go Kart is stored on an 8 ft by 5 ft pallet. Furthermore, a 5 ft by 5 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 30% of its inventory to pressure washers and Go Karts and sell at least twice as many generators as water pumps. 

Perform a monthly analysis using a linear programming model to maximize the company's net profit.  

Complete the following in a Word document and in an Excel workbook (or R). Submit both the Word document and the Excel workbook (or R script file) as attachments.         

1. In a Word document, write the mathematical formulation of the problem. 

2. Set up the linear programming formulation in an Excel workbook or R. 

3. Use the Excel Solver or R to solve the problem, and generate a 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 $170,000 allocated to the purchasing budget during the first month, the company should allocate additional money. If yes, how much 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.