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#3= In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function?

#3= In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function?

Exploring Economics
Exploring Economics
8th Edition
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:Robert L. Sexton
Chapter4: Demand, Supply, And Market Equilibrium
Section: Chapter Questions
Problem 7P
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#3= In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? 

When a company offers a new product or service, they estimate how much of that product or service people will want at different prices. This is referred to as the product or service demand. As the price of a product or service increases, the demand usually decreases, and this drives the price down. Companies use the estimated demand to determine how much of a product or service they are willing to supply at different prices. As the price of a product or service increases, companies are willing to supply more of it because they will earn more money. If you graph the demand and the supply curves on the same xy-plane, they will sometimes intersect at the point where the price and the supply are in equilibrium. Consider the scenario below. Yaseen is a local artist who wants to increase the amount of money she earns every month by selling at-home painting kits. These kits will include a photograph of the finished painting, a link and password to Yaseen's YouTube channel where she will provide detailed instructions and a step-by-step demonstration of how to create the painting. The kit also contains the canvas, and all the paints the buyer will need. Yaseen will create a new kit for sale each month. Yaseen estimates that the monthly demand for her painting kits can be modeled by the function f(x) = 0.02(x – 100)², where 0 <x < 85. The number of kits that Yaseen can supply each month is modeled by the function g(x) = 0.01x2 + 0.5x, where 0 < x < 100. The value of x represents the quantity of kits and the output of each function is the price. Use this information and what you know about quadratic functions and systems of non-linear equations to explore the questions below. 1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario? demand function of price decrease from 200 to 4.5 demand 0 to 85 Supply function g(100)=0.01x100^2=150 supply price increases as x quantity (paint increases) 2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. f(x)=0.02 (x-100)^2 , where 0 is less then or equal to x which is less than or equal to 85 g(x)=0.01 (x)^2+0.05x where 0 is less than or equal to x which is less then or equal to 100 , will be selling product at g(15)=0.01 (15)^2+0.05 x15 f(15) = 0.02(15 – 100)^2 = $ 144.5 (per unit of drawing kit). charge per unit ss funvtion=$9.75. dd= 144.5
Transcribed Image Text:When a company offers a new product or service, they estimate how much of that product or service people will want at different prices. This is referred to as the product or service demand. As the price of a product or service increases, the demand usually decreases, and this drives the price down. Companies use the estimated demand to determine how much of a product or service they are willing to supply at different prices. As the price of a product or service increases, companies are willing to supply more of it because they will earn more money. If you graph the demand and the supply curves on the same xy-plane, they will sometimes intersect at the point where the price and the supply are in equilibrium. Consider the scenario below. Yaseen is a local artist who wants to increase the amount of money she earns every month by selling at-home painting kits. These kits will include a photograph of the finished painting, a link and password to Yaseen's YouTube channel where she will provide detailed instructions and a step-by-step demonstration of how to create the painting. The kit also contains the canvas, and all the paints the buyer will need. Yaseen will create a new kit for sale each month. Yaseen estimates that the monthly demand for her painting kits can be modeled by the function f(x) = 0.02(x – 100)², where 0 <x < 85. The number of kits that Yaseen can supply each month is modeled by the function g(x) = 0.01x2 + 0.5x, where 0 < x < 100. The value of x represents the quantity of kits and the output of each function is the price. Use this information and what you know about quadratic functions and systems of non-linear equations to explore the questions below. 1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario? demand function of price decrease from 200 to 4.5 demand 0 to 85 Supply function g(100)=0.01x100^2=150 supply price increases as x quantity (paint increases) 2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work. f(x)=0.02 (x-100)^2 , where 0 is less then or equal to x which is less than or equal to 85 g(x)=0.01 (x)^2+0.05x where 0 is less than or equal to x which is less then or equal to 100 , will be selling product at g(15)=0.01 (15)^2+0.05 x15 f(15) = 0.02(15 – 100)^2 = $ 144.5 (per unit of drawing kit). charge per unit ss funvtion=$9.75. dd= 144.5
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