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After inventing a new type of bicycle pedal and receiving some financial backing, you decide to begin manufacturing three models: Type X, Y, and Z. To manufacture a Type X pedal requires 2 minutes on Machine I, 1 minute on Machine II, and 2 minutes on Machine III. A Type Y pedal requires 1 minute on Machine I, 3 minutes on Machine II, and 1 minute on Machine III. A Type Z pedal requires 1 minute on Machine I and 2 minutes each on Machines IlI and III. There are 3 hours available on Machine I, 5 hours available on Machine II, and 4 hours available on Machine II. How many pedals of each type should you make in order to use all of the available time as efficiently as possible? Directions 1. Assign variables as necessary and express the problem in terms of a system of equations. 2. Build the augmented matrix that corresponds to your answer in step 1. 3. Use your augmented matrix from step 2 to solve the problem. Show as many steps as necessary so one can follow your work.

After inventing a new type of bicycle pedal and receiving some financial backing, you decide to begin manufacturing three models: Type X, Y, and Z. To manufacture a Type X pedal requires 2 minutes on Machine I, 1 minute on Machine II, and 2 minutes on Machine III. A Type Y pedal requires 1 minute on Machine I, 3 minutes on Machine II, and 1 minute on Machine III. A Type Z pedal requires 1 minute on Machine I and 2 minutes each on Machines IlI and III. There are 3 hours available on Machine I, 5 hours available on Machine II, and 4 hours available on Machine II. How many pedals of each type should you make in order to use all of the available time as efficiently as possible? Directions 1. Assign variables as necessary and express the problem in terms of a system of equations. 2. Build the augmented matrix that corresponds to your answer in step 1. 3. Use your augmented matrix from step 2 to solve the problem. Show as many steps as necessary so one can follow your work.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement** After inventing a new type of bicycle pedal and receiving some financial backing, you decide to begin manufacturing three models: Type X, Y, and Z. To manufacture a Type X pedal requires 2 minutes on Machine I, 1 minute on Machine II, and 2 minutes on Machine III. A Type Y pedal requires 1 minute on Machine I, 3 minutes on Machine II, and 1 minute on Machine III. A Type Z pedal requires 1 minute on Machine I and 2 minutes each on Machines II and III. There are 3 hours available on Machine I, 5 hours available on Machine II, and 4 hours available on Machine III. How many pedals of each type should you make in order to use all of the available time as efficiently as possible? **Directions** 1. Assign variables as necessary and express the problem in terms of a system of equations. 2. Build the augmented matrix that corresponds to your answer in step 1. 3. Use your augmented matrix from step 2 to solve the problem. Show as many steps as necessary so one can follow your work.
Transcribed Image Text:**Problem Statement** After inventing a new type of bicycle pedal and receiving some financial backing, you decide to begin manufacturing three models: Type X, Y, and Z. To manufacture a Type X pedal requires 2 minutes on Machine I, 1 minute on Machine II, and 2 minutes on Machine III. A Type Y pedal requires 1 minute on Machine I, 3 minutes on Machine II, and 1 minute on Machine III. A Type Z pedal requires 1 minute on Machine I and 2 minutes each on Machines II and III. There are 3 hours available on Machine I, 5 hours available on Machine II, and 4 hours available on Machine III. How many pedals of each type should you make in order to use all of the available time as efficiently as possible? **Directions** 1. Assign variables as necessary and express the problem in terms of a system of equations. 2. Build the augmented matrix that corresponds to your answer in step 1. 3. Use your augmented matrix from step 2 to solve the problem. Show as many steps as necessary so one can follow your work.
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