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Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows:

Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows:

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows: Distance between Pairs of Offices Main В.1 В.2 В.3 В.4 В.5 Main office Branch 1 Branch 2 Branch 3 190 70 115 270 215 160 190 100 110 50 70 100 140 120 220 115 110 140 175 80 Branch 4 Branch 5 270 215 120 175 310 160 50 220 80 310 The management wishes to determine which pairs of offices should be directly connected by special phone lines in order to connect every branch office (directly or indirectly) to the main office at a minimum total cost. Describe the problem as a network problem and solve it with an appropriate algorithm that you have seen in the course
Transcribed Image Text:Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows: Distance between Pairs of Offices Main В.1 В.2 В.3 В.4 В.5 Main office Branch 1 Branch 2 Branch 3 190 70 115 270 215 160 190 100 110 50 70 100 140 120 220 115 110 140 175 80 Branch 4 Branch 5 270 215 120 175 310 160 50 220 80 310 The management wishes to determine which pairs of offices should be directly connected by special phone lines in order to connect every branch office (directly or indirectly) to the main office at a minimum total cost. Describe the problem as a network problem and solve it with an appropriate algorithm that you have seen in the course
Q2. The Quick Company has leamed that a competitor is planning to come out with a new kind of product with a great sales potential. Quick has been working on a similar product that had been scheduled to come to market in 20 months. However, research is nearly complete and Quick's management now wishes to rush the product out to meet the competition There are four nonoverlapping phases left to be accomplished, including the remaining research that currently is being conducted at a normal pace. However, each phase can instead be conducted at a priority or crash level to expedite completion, and these are the only levels that will be considered for the last three phases. The times required at these levels are given in the following table. (The times in parentheses at the normal level have been ruled out as too long.) Time Initiate Production Remaining Research Development Design of Manufacturing System and Level Distribution Normal 5 months Priority 4 months Crash (4 months) 3 months 2 months (7 months) 5 months 3 months (4 months) 2 months 1 month 2 months Management has allocated $50 million for these four phases. The cost of each phase at the different levels under consideration is as follows: Cost Initiate Design of Manufacturing System Production Remaining Research Development and Level Distribution Normal $5 million Priority $9 million $10 million Crash $14 million $15 million $14 million $19 million $6 million $9 million Management wishes to determine at which level to conduct each of the four phases to minimize the total time until the product can be marketed subject to the budget restriction of $50 million. Formulate and solve this problem as a shortest-path problem.
Transcribed Image Text:Q2. The Quick Company has leamed that a competitor is planning to come out with a new kind of product with a great sales potential. Quick has been working on a similar product that had been scheduled to come to market in 20 months. However, research is nearly complete and Quick's management now wishes to rush the product out to meet the competition There are four nonoverlapping phases left to be accomplished, including the remaining research that currently is being conducted at a normal pace. However, each phase can instead be conducted at a priority or crash level to expedite completion, and these are the only levels that will be considered for the last three phases. The times required at these levels are given in the following table. (The times in parentheses at the normal level have been ruled out as too long.) Time Initiate Production Remaining Research Development Design of Manufacturing System and Level Distribution Normal 5 months Priority 4 months Crash (4 months) 3 months 2 months (7 months) 5 months 3 months (4 months) 2 months 1 month 2 months Management has allocated $50 million for these four phases. The cost of each phase at the different levels under consideration is as follows: Cost Initiate Design of Manufacturing System Production Remaining Research Development and Level Distribution Normal $5 million Priority $9 million $10 million Crash $14 million $15 million $14 million $19 million $6 million $9 million Management wishes to determine at which level to conduct each of the four phases to minimize the total time until the product can be marketed subject to the budget restriction of $50 million. Formulate and solve this problem as a shortest-path problem.
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