Smith Publsihing Company has just recieved a 550 page manuscript from an author and wants to have it proof read by the end of the day. There are 3 readers who are avaliable to work on this project but because of other obligations the amount of time each can spend on this project is limited. The proof readers are Sam who is available for up to 6 hours today. Michael who is available for up to 4 hours today and Samantha who could work on it today for at most 5 hours. Because of the diffrences in experience and skill, each reader has diffrent proof reading speed, a diffrent accuracy rate per page and each charge Smith a different rate per page to proof-read. Sam proofs 64 pages per hour, has 97% accuracy rate and is paid .23 per page, michael proofs 48 pages/hour, has 96% accuarcy rate and is paid .25 per page and Samantha proofs 55 pages / hour, has 99% accuarcy rate and is paid .30 per page. Smith decided that they will be willing to spend at most $135 to have the manuscript proof-read. Formulate a linear program to determine how many pages smith should assign to each of the three proof readers in order to complete the job within budget and by the end of the day with maximizing the overall accuracy
Smith Publsihing Company has just recieved a 550 page manuscript from an author and wants to have it proof read by the end of the day. There are 3 readers who are avaliable to work on this project but because of other obligations the amount of time each can spend on this project is limited. The proof readers are Sam who is available for up to 6 hours today. Michael who is available for up to 4 hours today and Samantha who could work on it today for at most 5 hours.
Because of the diffrences in experience and skill, each reader has diffrent proof reading speed, a diffrent accuracy rate per page and each charge Smith a different rate per page to proof-read. Sam proofs 64 pages per hour, has 97% accuracy rate and is paid .23 per page, michael proofs 48 pages/hour, has 96% accuarcy rate and is paid .25 per page and Samantha proofs 55 pages / hour, has 99% accuarcy rate and is paid .30 per page. Smith decided that they will be willing to spend at most $135 to have the manuscript proof-read.
Formulate a linear program to determine how many pages smith should assign to each of the three proof readers in order to complete the job within budget and by the end of the day with maximizing the overall accuracy.
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