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1. Construct a table showing: • the number of the elements required for each item. the amount of each element available or the minimum requirements of each element. ● 2. State the objective function and determine the constraints for each element. 3. Produce a labelled graph showing the feasible region.

1. Construct a table showing: • the number of the elements required for each item. the amount of each element available or the minimum requirements of each element. ● 2. State the objective function and determine the constraints for each element. 3. Produce a labelled graph showing the feasible region.

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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Scenario 1: The head coach of Adelaide University Judo Club has designed two training programs to prepare their judokas for the upcoming regional championship taking place in sixteen weeks. Throughout the sixteen-week training period, three Judo coaches have been assigned to closely monitor each player's progress, adjust their training program as needed, and provide additional support and guidance to ensure that they are fully prepared for the regional championship. In programme A, Dylan designated a period of 2 hours on endurance and agility, incorporating long distance running, jump rope drills, and footwork exercises whereas Jason coaches for power and speed training for the duration of 4 hours which requires judokas to perform explosive movements such as polymetric jumps, sprints and deadlifts. On the other hand, Kai coaches for coordination and balance for the duration of 2 hours, which emphasises the fundamentals of Judo, such as breakfalls and isotonic movements. In programme B, the time period endurance and agility component increase by an additional 4 hours of training, the power and speed component reduce by 1 hour and the coordination and balance component increase by 2 hours of additional training. Program A costs $75 per week and Program B costs $107 per week. Dylan is available for a minimum of 10 hours and a maximum of 36 hours. Jason is limited to train for a maximum of 24 hours whereas Kai is contracted to train for a minimum of 8 hours. The head coach aims to maximise the profit while satisfying each coach's legal working hours requirements. 1. Construct a table showing: ● the number of the elements required for each item. the amount of each element available or the minimum requirements of each element. 2. State the objective function and determine the constraints for each element. 3. Produce a labelled graph showing the feasible region. 4. Find the optimal solution by considering the feasible points. 5. Determine the wastage or oversupply of elements for the optimal solution.
Transcribed Image Text:Scenario 1: The head coach of Adelaide University Judo Club has designed two training programs to prepare their judokas for the upcoming regional championship taking place in sixteen weeks. Throughout the sixteen-week training period, three Judo coaches have been assigned to closely monitor each player's progress, adjust their training program as needed, and provide additional support and guidance to ensure that they are fully prepared for the regional championship. In programme A, Dylan designated a period of 2 hours on endurance and agility, incorporating long distance running, jump rope drills, and footwork exercises whereas Jason coaches for power and speed training for the duration of 4 hours which requires judokas to perform explosive movements such as polymetric jumps, sprints and deadlifts. On the other hand, Kai coaches for coordination and balance for the duration of 2 hours, which emphasises the fundamentals of Judo, such as breakfalls and isotonic movements. In programme B, the time period endurance and agility component increase by an additional 4 hours of training, the power and speed component reduce by 1 hour and the coordination and balance component increase by 2 hours of additional training. Program A costs $75 per week and Program B costs $107 per week. Dylan is available for a minimum of 10 hours and a maximum of 36 hours. Jason is limited to train for a maximum of 24 hours whereas Kai is contracted to train for a minimum of 8 hours. The head coach aims to maximise the profit while satisfying each coach's legal working hours requirements. 1. Construct a table showing: ● the number of the elements required for each item. the amount of each element available or the minimum requirements of each element. 2. State the objective function and determine the constraints for each element. 3. Produce a labelled graph showing the feasible region. 4. Find the optimal solution by considering the feasible points. 5. Determine the wastage or oversupply of elements for the optimal solution.
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