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1. Find the total cost C(D) in dollars of producing D cans of sauce. 2. Use previously-determined information to find C (p), the total cost in dollars to produce enough cans to satisfy demand when the price is p dollars. (That is, replace D with an expression in terms of price.) 3. Profit is the defined as Revenue minus Cost. Find the total profit P(p) in dollars as a function of the unit price p in dollars. It is a good idea to use parentheses in order to avoid a sign error! 4. Use technology and calculus to determine the price at which profit is maximized and the profit that will be attained. There are multiple correct methods. Explain/show your approach and results in the space below.

1. Find the total cost C(D) in dollars of producing D cans of sauce. 2. Use previously-determined information to find C (p), the total cost in dollars to produce enough cans to satisfy demand when the price is p dollars. (That is, replace D with an expression in terms of price.) 3. Profit is the defined as Revenue minus Cost. Find the total profit P(p) in dollars as a function of the unit price p in dollars. It is a good idea to use parentheses in order to avoid a sign error! 4. Use technology and calculus to determine the price at which profit is maximized and the profit that will be attained. There are multiple correct methods. Explain/show your approach and results in the space below.

Calculus: Early Transcendentals
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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*3>OPTIMAL-PRICING-TO-MAXIMIZE-PROFITT The-Calculus-Canned-Corn-Company's-production-facility-hasa-weekly-overhead-cost-of-$1000 with-a-unit-cost of producing each-can-of. $0.66- plus the-cost of the can-itself (from part-2). The cost of the can is $6 from part 1
3 OPTIMAL PRICING TO MAXIMIZE PROFIT The Calculus Canned Corn Company's production facility has a weekly overhead cost of $1000 with a unit cost of producing each can of $0.66 plus the cost of the can itself (from part 2). 1. Find the total cost C(D) in dollars of producing D cans of sauce. 2. Use previously-determined information to find C (p), the total cost in dollars to produce enough cans to satisfy demand when the price is p dollars. (That is, replace D with an expression in terms of price.) 3. Profit is the defined as Revenue minus Cost. Find the total profit P(p) in dollars as a function of the unit price p in dollars. It is a good idea to use parentheses in order to avoid a sign error! 4. Use technology and calculus to determine the price at which profit is maximized and the profit that will be attained. There are multiple correct methods. Explain/show your approach and results in the space below.
Transcribed Image Text:3 OPTIMAL PRICING TO MAXIMIZE PROFIT The Calculus Canned Corn Company's production facility has a weekly overhead cost of $1000 with a unit cost of producing each can of $0.66 plus the cost of the can itself (from part 2). 1. Find the total cost C(D) in dollars of producing D cans of sauce. 2. Use previously-determined information to find C (p), the total cost in dollars to produce enough cans to satisfy demand when the price is p dollars. (That is, replace D with an expression in terms of price.) 3. Profit is the defined as Revenue minus Cost. Find the total profit P(p) in dollars as a function of the unit price p in dollars. It is a good idea to use parentheses in order to avoid a sign error! 4. Use technology and calculus to determine the price at which profit is maximized and the profit that will be attained. There are multiple correct methods. Explain/show your approach and results in the space below.
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