Question: A software consulting firm has received a large contract to develop a new airline reservation system for a major airline. In order to fulfil the contract, new hiring of programmer analysts, senior programmer analysts, and software engineers will be required. Each programmer analyst position will cost $40,000 in salary and benefits. Each senior programmer analyst position will cost $50,000 and each software engineer position $60,000. The airline has budgeted $1.2 million per year for the new hirings. If xj equals the number of persons hired for job category j (where j=1 corresponds to programmer analysts, etc.):
(a) Determine the equation which ensures that total new hires will 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) If exactly 10 programmer analysts are needed for the contract, what is the maximum number of of senior programmer analysts could be hired? Maximum number of software engineers?