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Answer :
Let's go through each part of the question step-by-step to help you understand the solution.
1. Approximate Cost Per Book:
- When 50 books are printed, the cost per book is calculated by adding the fixed cost to the variable cost for all books and then dividing by the number of books.
[tex]\[
\text{Cost per book for 50 books} = \frac{120 + 40 \times 50}{50} = \frac{2120}{50} = 42.4
\][/tex]
- Similarly, for 100 books, perform the same calculation:
[tex]\[
\text{Cost per book for 100 books} = \frac{120 + 40 \times 100}{100} = \frac{4120}{100} = 41.2
\][/tex]
2. Printing Enough Books to Make a Profit:
- Each book is sold for [tex]$8, and the cost per book varies. For the calculation, if we assume the cost per book gets close to variable cost ($[/tex]40), we find how many should be printed to break even:
[tex]\[
\text{Profit per book} = 8 - 40 = -32
\][/tex]
- The point where profit starts doesn't exist (since the profit per book is negative, indicating a misunderstanding in the setup). In this context, since profit calculation shows a negative break-even cost, further adjustment in cost management or pricing strategy would be needed.
3. Value of [tex]\( c(x) \)[/tex] When [tex]\( x = \frac{1}{2} \)[/tex]:
- Here, assuming a scenario where "x" represents some factor like a fraction of a book printed:
[tex]\[
c(x) = 120 + 40 \times \frac{1}{2} = 140
\][/tex]
- The [tex]\( c(x) \)[/tex] function evaluates the cost with half the typical fixed cost scenario applied, leading to an additional context-specific value which may represent cost under specific conditions.
4. End Behavior of the Function:
- As more books are printed, the fixed cost ([tex]$120) becomes less significant relative to the total cost, causing the average cost per book to approach the variable cost of printing each book ($[/tex]40). This means for a large number of books, the cost per book stabilizes around $40.
These explanations break down the solution in a straightforward way, highlighting how costs are structured based on a fixed and variable component. If you have further questions, feel free to ask!
1. Approximate Cost Per Book:
- When 50 books are printed, the cost per book is calculated by adding the fixed cost to the variable cost for all books and then dividing by the number of books.
[tex]\[
\text{Cost per book for 50 books} = \frac{120 + 40 \times 50}{50} = \frac{2120}{50} = 42.4
\][/tex]
- Similarly, for 100 books, perform the same calculation:
[tex]\[
\text{Cost per book for 100 books} = \frac{120 + 40 \times 100}{100} = \frac{4120}{100} = 41.2
\][/tex]
2. Printing Enough Books to Make a Profit:
- Each book is sold for [tex]$8, and the cost per book varies. For the calculation, if we assume the cost per book gets close to variable cost ($[/tex]40), we find how many should be printed to break even:
[tex]\[
\text{Profit per book} = 8 - 40 = -32
\][/tex]
- The point where profit starts doesn't exist (since the profit per book is negative, indicating a misunderstanding in the setup). In this context, since profit calculation shows a negative break-even cost, further adjustment in cost management or pricing strategy would be needed.
3. Value of [tex]\( c(x) \)[/tex] When [tex]\( x = \frac{1}{2} \)[/tex]:
- Here, assuming a scenario where "x" represents some factor like a fraction of a book printed:
[tex]\[
c(x) = 120 + 40 \times \frac{1}{2} = 140
\][/tex]
- The [tex]\( c(x) \)[/tex] function evaluates the cost with half the typical fixed cost scenario applied, leading to an additional context-specific value which may represent cost under specific conditions.
4. End Behavior of the Function:
- As more books are printed, the fixed cost ([tex]$120) becomes less significant relative to the total cost, causing the average cost per book to approach the variable cost of printing each book ($[/tex]40). This means for a large number of books, the cost per book stabilizes around $40.
These explanations break down the solution in a straightforward way, highlighting how costs are structured based on a fixed and variable component. If you have further questions, feel free to ask!
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