A hardware company is studying a plan to open a new distribution center in the southeast....

Transcribed Image Text:

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 Profit cost selling price Selling price-cost Pressure washer 320 500 180 Go-kart 380 720 340 Generator 410 7000 6590 Water pump 129 270 141 Solve the linear programming problem by using the Excel Solver, perform a sensitivity analysis, verify the model by applying duality theory, and interpret these results. Sensitivity Analysis: a) Sensitivity Analysis: Perform a sensitivity analysis on the primal model (the model from 1.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? 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 Profit cost selling price Selling price-cost Pressure washer 320 500 180 Go-kart 380 720 340 Generator 410 7000 6590 Water pump 129 270 141 Solve the linear programming problem by using the Excel Solver, perform a sensitivity analysis, verify the model by applying duality theory, and interpret these results. Sensitivity Analysis: a) Sensitivity Analysis: Perform a sensitivity analysis on the primal model (the model from 1.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?