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A manufacturing company makes two types of weiter Skis, a a Department Fabricating Finishing labor hrs per SKI Trick Ski Slalom SKI b 4 1 mum Good Maximum labor hrs Available per day 168' 36 Bh

A manufacturing company makes two types of weiter Skis, a a Department Fabricating Finishing labor hrs per SKI Trick Ski Slalom SKI b 4 1 mum Good Maximum labor hrs Available per day 168' 36 Bh

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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### Maximizing Profit in Ski Manufacturing A manufacturing company produces two types of water skis: trick skis and slalom skis. #### Labor Requirements and Availability In order to manufacture these skis, two departments are involved: Fabricating and Finishing. Below is the detailed table representing the labor hours required per ski and the maximum labor hours available per day: | Department | Labor hours per Ski | | Maximum labor hours available per day | |--------------|---------------------|---------------|---------------------------------------| | | Trick ski | Slalom ski | | | Fabricating | 6 | 4 | 168 | | Finishing | 3 | 2 | 36 | #### Problem Analysis **(a)** Given: - Profit on a trick ski: $40 - Profit on a slalom ski: $30 Calculate: 1. How many of each type of ski (trick & slalom) should be manufactured daily to maximize profit? 2. What is the maximum profit? **Solution Outline:** - Define the maximum profit equation. - Determine the mix of trick and slalom skis that maximizes this profit. **(b)** Scenario Change: Evaluate the effect on the production schedule and the maximum profit if the profit on a slalom ski is decreased to $25. **Solution Outline:** - Update the profit values in the maximum profit equation. - Recalculate the mix of skis and the maximum profit. **(c)** Scenario Change: Evaluate the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $35. **Solution Outline:** - Update the profit values in the maximum profit equation. - Recalculate the mix of skis and the maximum profit. This exercise emphasizes the importance of linear programming and optimization in manufacturing processes to achieve maximum profitability. By adjusting variables such as profit per unit, one can determine the optimal production mix that aligns with labor constraints and maximizes overall profit.
Transcribed Image Text:### Maximizing Profit in Ski Manufacturing A manufacturing company produces two types of water skis: trick skis and slalom skis. #### Labor Requirements and Availability In order to manufacture these skis, two departments are involved: Fabricating and Finishing. Below is the detailed table representing the labor hours required per ski and the maximum labor hours available per day: | Department | Labor hours per Ski | | Maximum labor hours available per day | |--------------|---------------------|---------------|---------------------------------------| | | Trick ski | Slalom ski | | | Fabricating | 6 | 4 | 168 | | Finishing | 3 | 2 | 36 | #### Problem Analysis **(a)** Given: - Profit on a trick ski: $40 - Profit on a slalom ski: $30 Calculate: 1. How many of each type of ski (trick & slalom) should be manufactured daily to maximize profit? 2. What is the maximum profit? **Solution Outline:** - Define the maximum profit equation. - Determine the mix of trick and slalom skis that maximizes this profit. **(b)** Scenario Change: Evaluate the effect on the production schedule and the maximum profit if the profit on a slalom ski is decreased to $25. **Solution Outline:** - Update the profit values in the maximum profit equation. - Recalculate the mix of skis and the maximum profit. **(c)** Scenario Change: Evaluate the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $35. **Solution Outline:** - Update the profit values in the maximum profit equation. - Recalculate the mix of skis and the maximum profit. This exercise emphasizes the importance of linear programming and optimization in manufacturing processes to achieve maximum profitability. By adjusting variables such as profit per unit, one can determine the optimal production mix that aligns with labor constraints and maximizes overall profit.
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