Atlantic Manufacturing has two manufacturing plants located in Halifax and Saint John. Product demand varies considerably from month to month, causing Atlantic extreme difficulty in workforce scheduling. Recently the company started hiring temporary workers supplied by Smith Unlimited, a company that specializes in providing temporary employees for firms in the Atlantic Canada. Smith Unlimited offered to provide temporary employees under two contract options that differ in terms of the length of employment and the cost. The two options are summarized:

Option Length of Employment Cost

$1$ One month $ $2450$

$2$ Two months $ $5750$

The longer contract periods are more expensive because Smith Unlimited experiences greater difficulty finding temporary workers who are willing to commit to longer work assignments. Over the next seven months, Atlantic projects the following needs for additional employees :

Month January February March April May June July

Employees Needed $14241827191512$

Each month, Atlantic can hire as many temporary employees as needed under each of the two options. For instance, if they hire four employees in January under Option $2,$ Smith Unlimited will supply them with four temporary workers who will work for two months: January and February. For these workers, Atlantic will have to pay $4($$$5750)=$$$23,000.$ Because of some merger negotiations under way, Atlantic does not want to commit to any contractual obligations for temporary employees that extend beyond July. Atlantic's quality control program requires each temporary employee to receive training at the time of hire. The training program is required even if the person worked for the Atlantic Manufacturing in the past. The company estimates that the cost of training is $ $925$ each time a temporary employee is hired. Thus, if a temporary employee is hired for one month, Atlantic will incur a training cost of $ $925,$ but will incur no additional training cost if the employee is on a two$-$month contract. $3($A$)$ Formulate an appropriate optimization model that can be used to determine the number of temporary employees that Atlantic Manufacturing should hire to meet the projected needs at a minimum total cost.