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O Question 11 < > A company produces very unusual CD's for which the variable cost is $7 per CD and the fixed costs 50000. They will sell the CD's for $75 each. Let a be the number of CD's produced. a. Write the total cost C as a function of the number of CD's produced. C = $ 50000+7x b. Write the total revenue R as a function of the number of CD's produced. R=$ 75x c. Write the total profit P as a function of the number of CD's produced. P= $ 68x- 50000

O Question 11 < > A company produces very unusual CD's for which the variable cost is $7 per CD and the fixed costs 50000. They will sell the CD's for $75 each. Let a be the number of CD's produced. a. Write the total cost C as a function of the number of CD's produced. C = $ 50000+7x b. Write the total revenue R as a function of the number of CD's produced. R=$ 75x c. Write the total profit P as a function of the number of CD's produced. P= $ 68x- 50000

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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**Question 11** A company produces very unusual CDs for which the variable cost is $7 per CD and the fixed costs are $50,000. They will sell the CDs for $75 each. Let \( x \) be the number of CDs produced. **a. Write the total cost \( C \) as a function of the number of CDs produced.** \( C = \$ 50000 + 7x \) **b. Write the total revenue \( R \) as a function of the number of CDs produced.** \( R = \$ 75x \) **c. Write the total profit \( P \) as a function of the number of CDs produced.** \( P = \$ (68x - 50000) \) **d. Find the number of CDs which must be produced to break even.** The number of CDs which must be produced to break even is \( \boxed{} \). Round to the nearest number of CDs. --- **Explanation of Graphs or Diagrams:** There are no graphs or diagrams present in the image. The image contains textual information related to a problem about cost, revenue, and profit functions for producing CDs. The problem is divided into parts (a through d) and asks for mathematical functions and the break-even point. 1. Part (a) requires the total cost function, which consists of fixed costs ($50,000) and variable costs ($7 per CD). 2. Part (b) requires the total revenue function, calculated as the selling price per CD ($75) multiplied by the number of CDs produced. 3. Part (c) requires the total profit function, derived from subtracting the total cost from the total revenue. 4. Part (d) asks for the calculation of the break-even point, where total revenue equals total cost. Note: The break-even calculation in part (d) is left incomplete for the user to solve.
Transcribed Image Text:**Question 11** A company produces very unusual CDs for which the variable cost is $7 per CD and the fixed costs are $50,000. They will sell the CDs for $75 each. Let \( x \) be the number of CDs produced. **a. Write the total cost \( C \) as a function of the number of CDs produced.** \( C = \$ 50000 + 7x \) **b. Write the total revenue \( R \) as a function of the number of CDs produced.** \( R = \$ 75x \) **c. Write the total profit \( P \) as a function of the number of CDs produced.** \( P = \$ (68x - 50000) \) **d. Find the number of CDs which must be produced to break even.** The number of CDs which must be produced to break even is \( \boxed{} \). Round to the nearest number of CDs. --- **Explanation of Graphs or Diagrams:** There are no graphs or diagrams present in the image. The image contains textual information related to a problem about cost, revenue, and profit functions for producing CDs. The problem is divided into parts (a through d) and asks for mathematical functions and the break-even point. 1. Part (a) requires the total cost function, which consists of fixed costs ($50,000) and variable costs ($7 per CD). 2. Part (b) requires the total revenue function, calculated as the selling price per CD ($75) multiplied by the number of CDs produced. 3. Part (c) requires the total profit function, derived from subtracting the total cost from the total revenue. 4. Part (d) asks for the calculation of the break-even point, where total revenue equals total cost. Note: The break-even calculation in part (d) is left incomplete for the user to solve.
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