Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa plant. Each EZ-Rider engine requires 6 hours of manufacturing time, and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2,100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 240 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 800 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2,400 for each EZ-Rider produced and $1.000 for each Lady-Sport produced. (a) Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit. (Let E represent the EZ-Rider model and let & represent the Lady-Sport model) 2.400 +1000 Max s.t. (E +(3 1✔ 2.100 L=240 2E + 2.5Ls 880 E, LE 0 (b) Solve the problem graphically. What is the optimal solution? (8.4)-(350.160 ✓ Engine manufacturing time Lady-Sport maximum Assembly and testing time

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 107P

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Transcribed Image Text:Embassy Motorcycles (EM) manufactures two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa plant. Each EZ-Rider engine requires 6 hours of manufacturing time, and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2,100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 240 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 880 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2,400 for each EZ-Rider produced and $1,800 for each Lady-Sport produced. (a) Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit. (Let & represent the EZ-Rider model let & represent the Lady-Sport model.) Max s.t. 6 2,400€ + 1800 ✓ E+ (3 X ] ✓ )² 4*2,100 Ls 240 2E+2.5Ls 880 E, LEO (b) Solve the problem graphically. What is the optimal solution? (E, L) = 350,160 ✔ ✓ Engine manufacturing time. Lady-Sport maximum Assembly and testing time

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