Suzanne is the general manager for a landscaping contractor. It is the busy season and she has more work than her crew can handle without overtime. She has $8$ jobs open at various locations in the county. The company has $6$ crews of laborers, along with an inventory of machinery. She has developed an estimate of the labor and machinery required at each job, along with the transportation time between jobs.

Suzanne wants to schedule the jobs so as to minimize overtime, while ensuring that every job is finished by its promise date. Her schedule must ensure that the appropriate machinery is available at each job. Her best option is to formulate this problems as