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)=0.01x^2+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. 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? How much should she charge for each of these kits based on her demand function? Show your work. 4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not? 5. What family of functions do f(x) and g(x) belong to? How do you know?
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
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
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)=0.01x^2+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.
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? How much should she charge for each of these kits based on her demand function? Show your work.
4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not?
5. What family of functions do f(x) and g(x) belong to? How do you know?
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