Simon Tech is a software company which specializes in customized programming services, particularly focusing in solutions for the banking industry. For any given project, the company may hire programmers in different countries of the world through one of three setups, depending on the project's duration: under setup A$,$ a programmer is hired for two months pto, $00$ per month; on deu sen B$,$ ale is hited for e months at Seriods er month, ape inder sell a

freelance programmer is usually not willing to commit to a project for a long period of time.

Over the first eight months of next year, Simon has estimated the following needs for programmers. January: $12,$ February: $25,$ March: $19,$ April: $17,$ May: $20,$ June: $14,$ July: $10,$ and August: $11.$ Simon wants to plan for staffing their projects up until August. The company's quality control program requires each programmer to receive training at the time of hire. The training program is required even if the programmer worked for the company in a past project. The cost of training is estimated at $$850$ per programmer hired, regardless of the length of the contract. Also, as a second component of quality control, Simon requires full$-$time employees to monitor the work of part$-$timers. These full$-$time employees do not work directly on the projects $($they are not part of the required number of programmers mentioned above$),$ are paid a bonus of $$2,000$ per month for their monitoring work, and each of them is in charge of monitoring a group of five or less programmers $($part$-$timers$)$ on any given month.

$$Formulate a linear program $($algebraic formulation$)$ to help Simon determine the number of programmers to hire each month on each setup $($contract$)$ type, as well as the number of full time employees dedicated to monitoring, in order to meet the estimated needs at the minimum total cost.

$$Build an Excel spreadsheet model of your algebraic formulation with appropriate use of SUMPRODUCT functions