A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Department Trick Ski Maximum Labor-Hours Available per Day 336 Slalom Ski Fabricating 8 6 Finishing 1 1 48 Answer parts (A), (B), and (C) below. C... (A) If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ 1920. The maximum occurs when 0 trick skis and 48 slalom skis are produced. (B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $35. The maximum profit $1680. The maximum occurs when 1680 trick skis and slalom skis are produced. decreases to increases to remains the same at
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Department Trick Ski Maximum Labor-Hours Available per Day 336 Slalom Ski Fabricating 8 6 Finishing 1 1 48 Answer parts (A), (B), and (C) below. C... (A) If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ 1920. The maximum occurs when 0 trick skis and 48 slalom skis are produced. (B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $35. The maximum profit $1680. The maximum occurs when 1680 trick skis and slalom skis are produced. decreases to increases to remains the same at
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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Transcribed Image Text:### Optimizing Production for Maximum Profit
A manufacturing company makes two types of water skis: a trick ski and a slalom ski. The relevant manufacturing data are given below:
#### Manufacturing Data Table
| Department | Trick Ski | Slalom Ski |
|--------------|-----------|------------|
| **Labor-Hours per Ski** | | |
| Fabricating | 8 | 6 |
| Finishing | 1 | 1 |
| **Maximum Labor-Hours Available per Day** | | |
| Fabricating | | 336 |
| Finishing | | 48 |
---
#### Problem Part (A):
**Question:** If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit?
**Solution:**
- The maximum profit is **$1920**.
- The maximum occurs when **0** trick skis and **48** slalom skis are produced.
---
#### Problem Part (B):
**Question:** Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $35.
**Solution:**
- The maximum profit **decreases to** **$1680**.
- The maximum occurs when **0** trick skis and **48** slalom skis are produced.
---
By analyzing the labor-hour constraints and adjusting for changes in profit margins, the company can optimize its production schedule to achieve maximum profitability.
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