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Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business nvolves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations. Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows For all (a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location to location 6. (Express your answers in the form X, where each x, represents the arc from node i to node j as either 1 or 0.) Xij = 0, 1. 35 min 12 3 18 p.m. 15 39 12 16 30 6 (b) How long (in minutes) does it take to make a delivery from location 1 to location 6? (Round your answer to the nearest whole number.) (c) Assume that it is now 1:00 p.m. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6? (Enter your answer in standard time. Round your answer to the nearest minute.)

Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business nvolves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations. Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows For all (a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location to location 6. (Express your answers in the form X, where each x, represents the arc from node i to node j as either 1 or 0.) Xij = 0, 1. 35 min 12 3 18 p.m. 15 39 12 16 30 6 (b) How long (in minutes) does it take to make a delivery from location 1 to location 6? (Round your answer to the nearest whole number.) (c) Assume that it is now 1:00 p.m. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6? (Enter your answer in standard time. Round your answer to the nearest minute.)

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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Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations. Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows 35 For all X;; = 0, 1. (a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 to location 6. (Express your answers in the form where each Xij represents the arc from node i to node j as either 1 or Xijr 0.) 30 12 p.m. 3 Need Help? Read It 18 15 39 12 16 5 (b) How long (in minutes) does it take to make a delivery from location 1 to location 6? (Round your answer to the nearest whole number.) min Show My Work (Required)? What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times. 30 (c) Assume that it is now 1:00 p.m. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6? (Enter your answer in standard time. Round your answer to the nearest minute.) Uploaded File (10 file maximum) No Files to Display Upload File
Transcribed Image Text:Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations. Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows 35 For all X;; = 0, 1. (a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 to location 6. (Express your answers in the form where each Xij represents the arc from node i to node j as either 1 or Xijr 0.) 30 12 p.m. 3 Need Help? Read It 18 15 39 12 16 5 (b) How long (in minutes) does it take to make a delivery from location 1 to location 6? (Round your answer to the nearest whole number.) min Show My Work (Required)? What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times. 30 (c) Assume that it is now 1:00 p.m. and that CARD just received a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location 1 is to be delivered to location 6? (Enter your answer in standard time. Round your answer to the nearest minute.) Uploaded File (10 file maximum) No Files to Display Upload File
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