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An equation can be written for a business to determine how much profit they will make. For an example, your business began selling sweatshirts at a cost of $10. The first year you sold 1,000 (great first year!). You decided to raise the selling price by $5 and found the total number sold decreased by 100 sweatshirts (see the table below). It costs $10 to produce 1 sweatshirt. vertex (35, 12,500) Selling Price $ (s) 2. W 10 15 20 25 Quantity Sold in 1 year (q) 1000 900 800 700 12000 Profit, P 10000 8000 6000 4000 2000 0 -2000 0 10 20 30 roblem? 40 Using some algebra, you determine the equation to represent the relationship between the selling price (s) and the profit (f(s)) (assuming you continue the trend of raising the price by $5 and selling 100 less) is f(s)=-20s +1400s-12,000. Above is the graph of the function. 1. What is 101 4. How many sweatshirts had to be sold to make a profit of $10,000? 30 of 70 selling price, s 5. What is the domain and range of the function in the context of this problem? 6. If you had a choice, what price would you set for the sweatshirts, and why?

An equation can be written for a business to determine how much profit they will make. For an example, your business began selling sweatshirts at a cost of $10. The first year you sold 1,000 (great first year!). You decided to raise the selling price by $5 and found the total number sold decreased by 100 sweatshirts (see the table below). It costs $10 to produce 1 sweatshirt. vertex (35, 12,500) Selling Price $ (s) 2. W 10 15 20 25 Quantity Sold in 1 year (q) 1000 900 800 700 12000 Profit, P 10000 8000 6000 4000 2000 0 -2000 0 10 20 30 roblem? 40 Using some algebra, you determine the equation to represent the relationship between the selling price (s) and the profit (f(s)) (assuming you continue the trend of raising the price by $5 and selling 100 less) is f(s)=-20s +1400s-12,000. Above is the graph of the function. 1. What is 101 4. How many sweatshirts had to be sold to make a profit of $10,000? 30 of 70 selling price, s 5. What is the domain and range of the function in the context of this problem? 6. If you had a choice, what price would you set for the sweatshirts, and why?

Advanced Engineering Mathematics
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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Profit Selling Sweatshirts An equation can be written for a business to determine how much profit they will make. For an example, your business began selling sweatshirts at a cost of $10. The first year you sold 1,000 (great first year!). You decided to raise the selling price by $5 and found the total number sold decreased by 100 sweatshirts (see the table below). It costs $10 to produce 1 sweatshirt. vertex (35, 12,500) Selling Price $ (s) 2. W 10 15 20 25 Quantity Sold in 1 year (q) 1000 900 800 700 12000 Profit, P 10000 8000 6000 4000 2000 0 -2000 9 10 20 30 roblem? 40 Using some algebra, you determine the equation to represent the relationship between the selling price (s) and the profit (f(s)) (assuming you continue the trend of raising the price by $5 and selling 100 less) is f(s)=-20s +1400s-12,000. Above is the graph of the function. 1. What is 10) 4. How many sweatshirts had to be sold to make a profit of $10,000? 50 ob 70 selling price, s 5. What is the domain and range of the function in the context of this problem? 6. If you had a choice, what price would you set for the sweatshirts, and why?
Transcribed Image Text:Profit Selling Sweatshirts An equation can be written for a business to determine how much profit they will make. For an example, your business began selling sweatshirts at a cost of $10. The first year you sold 1,000 (great first year!). You decided to raise the selling price by $5 and found the total number sold decreased by 100 sweatshirts (see the table below). It costs $10 to produce 1 sweatshirt. vertex (35, 12,500) Selling Price $ (s) 2. W 10 15 20 25 Quantity Sold in 1 year (q) 1000 900 800 700 12000 Profit, P 10000 8000 6000 4000 2000 0 -2000 9 10 20 30 roblem? 40 Using some algebra, you determine the equation to represent the relationship between the selling price (s) and the profit (f(s)) (assuming you continue the trend of raising the price by $5 and selling 100 less) is f(s)=-20s +1400s-12,000. Above is the graph of the function. 1. What is 10) 4. How many sweatshirts had to be sold to make a profit of $10,000? 50 ob 70 selling price, s 5. What is the domain and range of the function in the context of this problem? 6. If you had a choice, what price would you set for the sweatshirts, and why?
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