Tech, with a student population of 30,000, is located in a small college town in Virginia. DirectCast Cable TV has a small service staff that is sufficient to handle installations and TV hookups for almost the entire year. However, for the month-long period right before and during the beginning of fall semester in August, when all the students return, the cable TV service is overwhelmed and must bring in an additional 14 technicians from other company offices. The DirectCast offices in the following seven cities have available service technicians to loan, as shown: City Available Technicians Distance (mi.) Cost ($) Richmond 4 211 3,400 Charlotte 3 173 3,920 Atlanta 5 410 4,760 Greensboro 2 152 3,560 DC 6 263 4,980 Nashville 3 414 4,050 Norfolk 2 302 3,240 This table also shows the distances (in miles) from the cities to the town where Tech is located, and the cost for relocating a technician for 1 month, which includes monthly salary and a bonus. The national DirectCast office incurs this monthly cost. Because most of the technicians will commute to their homes at least once a week for a few days, the company wants to minimize the total distance incurred by its employees, but it would also like to keep its labor costs to $60,000 or less. Formulate a linear programming model for this problem (The mathematical model can be either typed or handwritten. Do not put the mathematical model inside the excel file). Solve the model by using the computer (Please submit the excel file containing the solution and the solver configuration along with the report) and report the optimal solution and objective function in your report. If DirectCast wants to minimize its cost and not the distance traveled, how would this affect the solution?
Tech, with a student population of 30,000, is located in a small college town in Virginia. DirectCast Cable TV has a small service staff that is sufficient to handle installations and TV hookups for almost the entire year. However, for the month-long period right before and during the beginning of fall semester in August, when all the students return, the cable TV service is overwhelmed and must bring in an additional 14 technicians from other company offices. The DirectCast offices in the following seven cities have available service technicians to loan, as shown:
|
City |
Available Technicians |
Distance (mi.) |
Cost ($) |
|
Richmond |
4 |
211 |
3,400 |
|
Charlotte |
3 |
173 |
3,920 |
|
Atlanta |
5 |
410 |
4,760 |
|
Greensboro |
2 |
152 |
3,560 |
|
DC |
6 |
263 |
4,980 |
|
Nashville |
3 |
414 |
4,050 |
|
Norfolk |
2 |
302 |
3,240 |
This table also shows the distances (in miles) from the cities to the town where Tech is located, and the cost for relocating a technician for 1 month, which includes monthly salary and a bonus. The national DirectCast office incurs this monthly cost. Because most of the technicians will commute to their homes at least once a week for a few days, the company wants to minimize the total distance incurred by its employees, but it would also like to keep its labor costs to $60,000 or less.
- Formulate a linear programming model for this problem (The mathematical model can be either typed or handwritten. Do not put the mathematical model inside the excel file).
- Solve the model by using the computer (Please submit the excel file containing the solution and the solver configuration along with the report) and report the optimal solution and objective function in your report.
- If DirectCast wants to minimize its cost and not the distance traveled, how would this affect the solution?
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