2) ABC Company has learned that its competitor is planning to come out with a new product with great sales potential. ABC has been working on a similar product that had been scheduled to come to market in 20 months. Now, the research phase is nearly complete and ABC's management wishes to rush the product out to meet the competition. Each project phase (research, development, design of the manufacturing system, and initiation of production and distribution) can be conducted at either a normal pace, at a priority pace, or at an expedited pace. However, the normal pace has been ruled out as too slow for the last three phases. The times required at each pace are below. Pace Development Remaining Research Design of Mfg. System Initiate Production & Distribution Normal Priority Expedited 5 months 4 months 2 months 3 months 2 months 5 months 3 months 2 months 1 month Management has allocated $30 million for all four phases. The cost of each phase at different paces is given below. Pace Remaining Research Development Design of Mfg. System Initiate Production & Distribution Normal Priority Expedited $3 million $6 million $9 million $6 million $9 million $9 million $12 million $3 million $6 million Management wants to determine the pace at which cach of the four phases should be conducted. a. Formulate this problem as a shortest path problem: Draw and clearly label the network. b. What is the optimal solution? You do not need to use an algorithm (i.e., you may solve by inspection) 2) ABC Company has learned that its competitor is planning to come out with a new product with great sales potential. ABC has been working on a similar product that had been scheduled to come to market in 20 months. Now, the research phase is nearly complete and ABC's management wishes to rush the product out to meet the competition. Each project phase (research, development, design of the manufacturing system, and initiation of production and distribution) can be conducted at either a normal pace, at a priority pace, or at an expedited pace. However, the normal pace has been ruled out as too slow for the last three phases. The times required at each pace are below. Pace Development Remaining Research Design of Mfg. System Initiate Production & Distribution Normal Priority Expedited 5 months 4 months 2 months 3 months 2 months 5 months 3 months 2 months 1 month Management has allocated $30 million for all four phases. The cost of each phase at different paces is given below. Pace Remaining Research Development Design of Mfg. System Initiate Production & Distribution Normal Priority Expedited $3 million $6 million $9 million $6 million $9 million $9 million $12 million $3 million $6 million Management wants to determine the pace at which cach of the four phases should be conducted. a. Formulate this problem as a shortest path problem: Draw and clearly label the network. b. What is the optimal solution? You do not need to use an algorithm (i.e., you may solve by inspection)