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Suppose you're making hand-carved birdhouses to sell in an online store. The price function for how much you sell them for is p (x) = 60 - .05x and the cost of building a birdhouses is C (x) = x (25 – .01x). - • What is the revenue function R (x)? • What is the profit function P (x)?

Suppose you're making hand-carved birdhouses to sell in an online store. The price function for how much you sell them for is p (x) = 60 - .05x and the cost of building a birdhouses is C (x) = x (25 – .01x). - • What is the revenue function R (x)? • What is the profit function P (x)?

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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Question
In an economics setting we often see P = R – C where P is the profit a business makes, Ris the revenue brought in from sales, and C is the overall cost of operating the business. As a simplistic example, if we have a cost of C = $3000 to make some amount of product, and we sell that for R= $5000 in revenue, we have made P = R – C = $5000 – $3000 = $2000 as a profit. In some cases, the price you can sell a product for is dependent on how many you sell, because of the relationship between supply and demand - when you have fewer of them available, you can sell them for a higher price, for example. If we have a price function p (x), the revenue function will be R (x) = x · p (x) because the money brought in will be the number of units sold times the price of each unit. The cost of production, measured per unit, may decrease based on how many you produce, if you can purchase materials in bulk, but this requires a greater initial investment. Often we can use information about how the cost and revenue vary depending on many units are sold, to get information how to maximize profit. Suppose you're making hand-carved birdhouses to sell in an online store. The price function for how much you sell them for is p (x) = 60 – .05x and the cost of building x birdhouses is C (x) = x (25 – .01x). • What is the revenue function R (x)? • What is the profit function P (x)?
Transcribed Image Text:In an economics setting we often see P = R – C where P is the profit a business makes, Ris the revenue brought in from sales, and C is the overall cost of operating the business. As a simplistic example, if we have a cost of C = $3000 to make some amount of product, and we sell that for R= $5000 in revenue, we have made P = R – C = $5000 – $3000 = $2000 as a profit. In some cases, the price you can sell a product for is dependent on how many you sell, because of the relationship between supply and demand - when you have fewer of them available, you can sell them for a higher price, for example. If we have a price function p (x), the revenue function will be R (x) = x · p (x) because the money brought in will be the number of units sold times the price of each unit. The cost of production, measured per unit, may decrease based on how many you produce, if you can purchase materials in bulk, but this requires a greater initial investment. Often we can use information about how the cost and revenue vary depending on many units are sold, to get information how to maximize profit. Suppose you're making hand-carved birdhouses to sell in an online store. The price function for how much you sell them for is p (x) = 60 – .05x and the cost of building x birdhouses is C (x) = x (25 – .01x). • What is the revenue function R (x)? • What is the profit function P (x)?
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