Grafton Metalworks Company produces metal alloys from six different ores it mines. The 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 16 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 ($) 5 Richmond Charlotte Atlanta Greensboro DC Nashville Norfolk 4 3 5 2 6 3 2 211 173 410 152 263 414 302 3.400 3,920 4.760 3,560 4.980 4,050 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. Since 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 $40,000 or less. Formulate a linear programming model for this