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 company’s finance department has notified the management that such an investment is advised only if the new facility generates at least a net profit of $400,000 in the first year of its operation.

The company estimates that the monthly rent and utilities will be about $20,000. Also, the management plans to sign a contract with a local company to rent a number of forklifts for a monthly fee of $1,500. Furthermore, the company estimates that it will have to spend an additional $420,000 annually to hire a manager, a secretary, and five full time employees. The table below describes how much each of the products cost the company (including transportation costs):

            Item                                          Cost in dollars

• Pressure washer                        $320.00 

• Go-kart                                         $380.00 

• (Case of 5 Water Pumps)         $645.00

The company has set aside a budget of $170,000 for merchandise each month to be sent to the new location. The selling prices (per unit) for each item are given below:

           Item                               Selling price

• Pressure washer             $499.99

• Go-kart                              $719.99

• Generator                         $699.99

• Water pump                     $269.99

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 (there are five water pumps in each case).

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. Then determine whether the company should open its new branch in southeast.

Please complete the following in a Word document

[GRADING RUBRIC]

1. Describe the three components of the LP problem. (5 points)

2. Write the formulation of the problem. (5 points)

3. Solve the problem in an Excel workbook by using the Excel Solver, and generate both the Answer and Sensitivity reports of Excel. (30 points)

4. Write the optimal solution in the word document, and explain whether the condition set by the company’s finance department has been satisfied. (5 points)

5. One of the decision variables has an optimal value of zero. In the word document, explain what the selling price of that item should be in order for this optimal solution value to change. (5 points)

6. In the word document explain whether, in addition to the $170,000 allocated to the merchandise 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 profit to increase as a consequence? (5 points)

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 size of your recommended warehouse in square feet, and indicate how much this change in the size of the warehouse will contribute to the yearly profit. (5 points)

Submissions must include both the completed Excel workbook and the completed Word document as attachments. Please note that incomplete submissions are not accepted.