How many thingamabobs should Yaster Inc. produce and sell in order to maximize profit?
How many thingamabobs should Yaster Inc. produce and sell in order to maximize profit?
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:### Maximizing Production and Sales for Profit
**Question:**
**Use the Sales information above to answer this question:**
How many thingamabobs should Yaster Inc. produce and sell in order to maximize profit?
**Answer:**
\_\_\_\_\_\_\_\_\_\_ thingamabobs. Round to the nearest thingamabobs.
**Input Box:**
To find the maximum profit, you'll need to use the sales data provided (not visible in this text but assumed to be detailed above). Analyze the production and sales figures to determine the optimal number of thingamabobs that should be produced and sold.
---
**Explanation:**
For educational purposes, ensure you understand the underlying factors that affect the profit calculation, such as cost of production per unit, selling price per unit, and total revenue. In a real-world scenario, graphical data such as profit curves, cost curves, and revenue curves would be analyzed if provided. Unfortunately, there are no graphs or diagrams included in the provided text.
![### Thingamabob Sales
Yaster Inc. is trying to enter the thingamabob market. The research department established the following price-demand, cost, and revenue functions:
\[
\begin{array}{|c|c|}
\hline
p(x) = 57 - 1.14x & \text{Price-demand function} \\
\hline
C(x) = 215 + 11x & \text{Cost function} \\
\hline
R(x) = xp(x) = x(57 - 1.14x) & \text{Revenue function} \\
\hline
\end{array}
\]
where \( x \) is in thousands of thingamabobs and \( C(x) \) and \( R(x) \) are in thousands of dollars. The price \( p(x) \) is the price in dollars of one thingamabob when the demand is \( x \) thousand thingamabobs. All three functions have the domain \( 1 \leq x \leq 50 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea6ddd78-5d51-4e2d-8762-122e3c25fe21%2F9f428704-14a6-4490-9fd4-9fb3a1bfbd4c%2F9hrattc_processed.png&w=3840&q=75)
Transcribed Image Text:### Thingamabob Sales
Yaster Inc. is trying to enter the thingamabob market. The research department established the following price-demand, cost, and revenue functions:
\[
\begin{array}{|c|c|}
\hline
p(x) = 57 - 1.14x & \text{Price-demand function} \\
\hline
C(x) = 215 + 11x & \text{Cost function} \\
\hline
R(x) = xp(x) = x(57 - 1.14x) & \text{Revenue function} \\
\hline
\end{array}
\]
where \( x \) is in thousands of thingamabobs and \( C(x) \) and \( R(x) \) are in thousands of dollars. The price \( p(x) \) is the price in dollars of one thingamabob when the demand is \( x \) thousand thingamabobs. All three functions have the domain \( 1 \leq x \leq 50 \).
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