9.25 Reducing Time to Develop Software i36 The firm ALCSOFT develops software for telecommunication companies. It is currently working on developing software for which 54 weeks of work have been estimated. Its customer is willing to increase the project budget by $50,000 if ALCSOFT manages to cut this time by at least 30 % with this increase. The manager of the project in question has analysed the possibilities of cutting the time to develop the software according to the increase in expense in the three funda- mental project resources: personnel, software and hardware. The Project Manager has concluded that for every $10,000 invested in personnel, the time is cut by 5 weeks, and if the same amount is invested in software, it is cut by 3 weeks, and if it is invested in hardware, the time is reduced by 2 weeks. Nonetheless, according to the current combination of resources, it will not be possible to invest more than $20,000 in personnel, and the same limit applies for software. (a) Consider this problem with dynamic programming to describe the phase, the state, the decision variable and the recursive function. Specify how the en+1 is calculated and what the possible states in each phase and the feasible decisions to be made are (b) Solve the