A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.2x + 7500, osxs 50,000 1 (68,000x - x²), osxs 50,000 10,000 (a) Write the profit function for this situation. P. (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.) increasing decreasing (c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit. hamburgers Explain your reasoning. O The restaurant makes the same amount of money no matter how many hamburgers are sold. O Because the function is always decreasing, the maximum profit occurs at this value of x. Because the function changes from increasing to decreasing at this value of x, the maximum profit occurs at this value. Because the function is always increasing, the maximum profit occurs at this value of x. O Because the function changes from decreasing to increasing at this value of x, the maximum profit occurs at this value.
A fast-food restaurant determines the cost and revenue models for its hamburgers. C = 0.2x + 7500, osxs 50,000 1 (68,000x - x²), osxs 50,000 10,000 (a) Write the profit function for this situation. P. (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.) increasing decreasing (c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit. hamburgers Explain your reasoning. O The restaurant makes the same amount of money no matter how many hamburgers are sold. O Because the function is always decreasing, the maximum profit occurs at this value of x. Because the function changes from increasing to decreasing at this value of x, the maximum profit occurs at this value. Because the function is always increasing, the maximum profit occurs at this value of x. O Because the function changes from decreasing to increasing at this value of x, the maximum profit occurs at this value.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem Statement:**
A fast-food restaurant determines the cost and revenue models for its hamburgers.
- Cost function: \( C = 0.2x + 7500, \quad 0 \leq x \leq 50,000 \)
- Revenue function: \( R = \frac{1}{10,000}(68,000x - x^2), \quad 0 \leq x \leq 50,000 \)
**Tasks:**
(a) Write the profit function for this situation.
- \( P = \) [Input Equation]
(b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.)
- Increasing: [Input Interval]
- Decreasing: [Input Interval]
(c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit.
- [Input Number] hamburgers
**Explain your reasoning:**
- The restaurant makes the same amount of money no matter how many hamburgers are sold.
- Because the function is always decreasing, the maximum profit occurs at this value of \( x \).
- Because the function changes from increasing to decreasing at this value of \( x \), the maximum profit occurs at this value.
- Because the function is always increasing, the maximum profit occurs at this value of \( x \).
- Because the function changes from decreasing to increasing at this value of \( x \), the maximum profit occurs at this value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa855ab5f-3c9d-4f99-b3de-79b498a6b4b6%2F8afb5d1e-0538-4d42-9be2-d7954c503323%2F6ip5zj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A fast-food restaurant determines the cost and revenue models for its hamburgers.
- Cost function: \( C = 0.2x + 7500, \quad 0 \leq x \leq 50,000 \)
- Revenue function: \( R = \frac{1}{10,000}(68,000x - x^2), \quad 0 \leq x \leq 50,000 \)
**Tasks:**
(a) Write the profit function for this situation.
- \( P = \) [Input Equation]
(b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answers using interval notation.)
- Increasing: [Input Interval]
- Decreasing: [Input Interval]
(c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit.
- [Input Number] hamburgers
**Explain your reasoning:**
- The restaurant makes the same amount of money no matter how many hamburgers are sold.
- Because the function is always decreasing, the maximum profit occurs at this value of \( x \).
- Because the function changes from increasing to decreasing at this value of \( x \), the maximum profit occurs at this value.
- Because the function is always increasing, the maximum profit occurs at this value of \( x \).
- Because the function changes from decreasing to increasing at this value of \( x \), the maximum profit occurs at this value.
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