Mr. Hann Is Trying To Decide How Many New Copies Of A Book To Order For His Students. Each Book Weighs 6 Ounces.Which Table Contains Only Viable Solutions If $b$ Represents The Number Of Books He Orders And $w$ Represents The
Introduction
Mr. Hann, a diligent educator, is faced with a crucial decision regarding the number of new copies of a book to order for his students. Each book weighs 6 ounces, and he needs to determine the optimal quantity to meet the demands of his students while minimizing unnecessary expenses. In this scenario, we will explore the mathematical approach to finding viable solutions for Mr. Hann's dilemma.
Understanding the Problem
Let's break down the problem and define the variables involved:
- b: The number of books Mr. Hann orders
- w: The weight of each book in ounces (6 ounces)
- Total Weight: The total weight of the books ordered by Mr. Hann
The problem can be represented mathematically as:
Total Weight = b × w
Since each book weighs 6 ounces, we can substitute w = 6 into the equation:
Total Weight = b × 6
Constraints and Assumptions
To find viable solutions, we need to consider the constraints and assumptions involved in the problem:
- Non-Negativity Constraint: The number of books ordered (b) must be a non-negative integer, as Mr. Hann cannot order a negative number of books.
- Weight Constraint: The total weight of the books ordered must be less than or equal to the maximum weight capacity of the storage space or transportation vehicle.
- Assumption: We assume that the weight of each book is constant at 6 ounces.
Table of Viable Solutions
Based on the constraints and assumptions, we can create a table of viable solutions for Mr. Hann's book orders:
| Number of Books (b) | Total Weight (b × 6) |
|---|---|
| 0 | 0 |
| 1 | 6 |
| 2 | 12 |
| 3 | 18 |
| 4 | 24 |
| 5 | 30 |
| 6 | 36 |
| 7 | 42 |
| 8 | 48 |
| 9 | 54 |
| 10 | 60 |
Analyzing the Table
From the table, we can observe the following:
- The total weight of the books ordered increases linearly with the number of books ordered.
- The minimum total weight is 0, which occurs when Mr. Hann orders 0 books.
- The maximum total weight is 60, which occurs when Mr. Hann orders 10 books.
Conclusion
In conclusion, the table of viable solutions provides a mathematical approach to finding the optimal number of books to order for Mr. Hann's students. By considering the constraints and assumptions, we can determine the feasible solutions that meet the demands of the students while minimizing unnecessary expenses.
Recommendations
Based on the analysis, we recommend the following:
- Mr. Hann should order at least 1 book to meet the minimum demand of his students.
- Mr. Hann should consider ordering up to 10 books to meet the maximum demand of his students.
- Mr. Hann should weigh the costs and benefits of ordering different quantities of books to determine the optimal solution.
Q: What is the minimum number of books Mr. Hann should order?
A: The minimum number of books Mr. Hann should order is 1, as this will meet the minimum demand of his students.
Q: What is the maximum number of books Mr. Hann should order?
A: The maximum number of books Mr. Hann should order is 10, as this will meet the maximum demand of his students.
Q: How can Mr. Hann determine the optimal number of books to order?
A: Mr. Hann can determine the optimal number of books to order by weighing the costs and benefits of ordering different quantities of books. He should consider factors such as the cost of the books, the demand of his students, and the storage space available.
Q: What is the total weight of the books ordered when Mr. Hann orders 5 books?
A: The total weight of the books ordered when Mr. Hann orders 5 books is 5 × 6 = 30 ounces.
Q: Can Mr. Hann order a fraction of a book?
A: No, Mr. Hann cannot order a fraction of a book. The number of books ordered must be a non-negative integer.
Q: What is the weight of each book in pounds?
A: The weight of each book is 6 ounces, which is equivalent to 0.375 pounds.
Q: How can Mr. Hann ensure that he has enough storage space for the books?
A: Mr. Hann can ensure that he has enough storage space for the books by measuring the storage space available and comparing it to the total weight of the books ordered.
Q: What is the total weight of the books ordered when Mr. Hann orders 10 books?
A: The total weight of the books ordered when Mr. Hann orders 10 books is 10 × 6 = 60 ounces.
Q: Can Mr. Hann order more than 10 books?
A: Yes, Mr. Hann can order more than 10 books, but he should consider the costs and benefits of doing so. He should also ensure that he has enough storage space available.
Q: How can Mr. Hann minimize unnecessary expenses when ordering books?
A: Mr. Hann can minimize unnecessary expenses when ordering books by ordering the optimal number of books, considering the costs and benefits of different quantities, and ensuring that he has enough storage space available.
Q: What is the relationship between the number of books ordered and the total weight of the books?
A: The total weight of the books ordered is directly proportional to the number of books ordered. As the number of books ordered increases, the total weight of the books also increases.