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. cost selling price pressure washer 320 500 go-kart 380 720 generator 410 7000 water pump 129 270 a)Build linear programming models that successfully address real-world operations research scenarios b)Optimize linear objective functions using the simplex method and applying duality theory c)Interpret the results of sensitivity analysis to investigate how changes in the parameters of a linear programming problem affect its optimal solution Communicate operations research and mathematical concepts effectively to a variety of audiences
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.
| cost | selling price | |
| pressure washer | 320 | 500 |
| go-kart | 380 | 720 |
| generator | 410 | 7000 |
| water pump | 129 | 270 |
a)Build linear programming models that successfully address real-world operations research scenarios
b)Optimize linear objective functions using the simplex method and applying duality theory
c)Interpret the results of sensitivity analysis to investigate how changes in the parameters of a linear programming problem affect its optimal solution
Communicate operations research and mathematical concepts effectively to a variety of audiences
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