40) Personnel Hiring - The management of a software firm wishes to develop a reservation system for an airline. In order to fulfill the contract, additional hiring of analysts, programmers, and engineers may be required. The cost of annual salary and benefits for an analyst, a programmer, and an engineer position are $30,000, $50,000, and $80,000, respectively. The airline's budget is $1.2 million per year for the additional hiring. If x equals the number of persons hired for the job category i (where i = a, p, e corresponds to analyst, programmer and engineer, respectively): a. Determine the equation that ensures total new hires exactly consume the budget. b. If it were desired to spend the entire budget on one type of position, how many persons of each type could be hired? c. 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