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 projects duration: under setup A, a programmer is hired for two months at $2,300 per month; under setup B, a programmer is hired for three months at $2,400 per month; and under setup C, a programmer is hired for four months at $2,500 per month. The longer contract periods are more expensive as usually 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 companys 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. Xij : Number of Programers under contract ! starting in month j algebraic formulation with variable and constrains