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 $$170,000$ for the new location. The selling prices $($per unit$)$ for each item are given in the table below: $2$ Item Selling Price $($in Dollars$)$ Pressure washer $499\mathrm{.}99$ Go$-$kart $729\mathrm{.}99$ Generator $700\mathrm{.}99$ Water pump $269\mathrm{.}99$ Table $2$: Revenues of products in dollars Other than the budget, another of the company$$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.