The management of a software firm wishes to develop an airline reservation system. In order to fulfill the contract, additional hiring of analysts, programmers, and engineers may be required. Each analyst, each programmer, and each engineer position will cost $30,000, $50,000 and $80,000 in salary and benefits, respectively.The airline budget is $1.2 millions per year for the additional hiring. If Xj equals the number of persons hired for the job catefgory j (where j=a,p,e corresponds to analyst, programmer, and engineer, respectively).
1. Determine the equation that ensures total new hires will exactly consume the budget
2. If it were desired to spend the entire budget on one type of position, how many persons of each type could be hired?
3. Determine the number of analysts, programmers, and engineers to be hired if for every one engineer. 2 programmers and 2 analysts are needed for the contract.