RELATED RATES: IN San Francisco, the price p (in dollars per pound) of lobster and the quantity available x (in thousands of pounds) is given by the equation: xp+12x+8p=1790 On a particular day the local lobster suppliers can make 38 thousand pounds of lobster available. a) Find the corresponding price p. b) Suppose at this supply level, the supply is decreasing at a rate of 1.2 thousand lbs. of lobste per day. Find the corresponding rate of change of the price of lobster. (Use Calculus-based methods
RELATED RATES: IN San Francisco, the price p (in dollars per pound) of lobster and the quantity available x (in thousands of pounds) is given by the equation: xp+12x+8p=1790 On a particular day the local lobster suppliers can make 38 thousand pounds of lobster available. a) Find the corresponding price p. b) Suppose at this supply level, the supply is decreasing at a rate of 1.2 thousand lbs. of lobste per day. Find the corresponding rate of change of the price of lobster. (Use Calculus-based methods
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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![**Related Rates Problem: Lobster Pricing and Supply in San Francisco**
**Context:** In San Francisco, the price \( p \) (in dollars per pound) of lobster and the quantity available \( x \) (in thousands of pounds) is determined by the equation:
\[ xp + 12x + 8p = 1790 \]
**Situation:** On a particular day, the local lobster suppliers can make 38 thousand pounds of lobster available.
**Tasks:**
a) **Determine the Price \( p \):**
- Given \( x = 38 \) (thousand pounds), find the corresponding price \( p \).
b) **Analyze the Rate of Change:**
- Suppose at this supply level, the supply is **decreasing** at a rate of 1.2 thousand pounds of lobster per day. Find the corresponding **rate of change of the price** of lobster. (Use Calculus-based methods.)
This problem involves understanding the relationship between price and supply and how changes in supply affect pricing using calculus concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94a522d8-ef89-4b5b-a14c-d37c6cf2440e%2Ff317f256-f9fe-4484-bb03-a029ee54e6aa%2Fcd88n7_processed.png&w=3840&q=75)
Transcribed Image Text:**Related Rates Problem: Lobster Pricing and Supply in San Francisco**
**Context:** In San Francisco, the price \( p \) (in dollars per pound) of lobster and the quantity available \( x \) (in thousands of pounds) is determined by the equation:
\[ xp + 12x + 8p = 1790 \]
**Situation:** On a particular day, the local lobster suppliers can make 38 thousand pounds of lobster available.
**Tasks:**
a) **Determine the Price \( p \):**
- Given \( x = 38 \) (thousand pounds), find the corresponding price \( p \).
b) **Analyze the Rate of Change:**
- Suppose at this supply level, the supply is **decreasing** at a rate of 1.2 thousand pounds of lobster per day. Find the corresponding **rate of change of the price** of lobster. (Use Calculus-based methods.)
This problem involves understanding the relationship between price and supply and how changes in supply affect pricing using calculus concepts.
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