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 inereases, companies are willing to supply more of it because they will eam 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 carns every month by selling t-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 instructioes 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 ereate a new kit for sale ench moeth. Yaseen estimates that the monthly demand for her painting kits can be modeled by the function f(x) 0.02(x-100), where 0SxS 85. The number of kits that Yaseen can supply each month is modeled by the function g(x) = 0.01x + 0.5x, where 0SIS 100. The value of x represents the quantity of kits and the output of cach function is the price. Ue 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 seenario? 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 mach should she charge for each of these kits based on her demand function? Show your work. (x)=0.02 (x-100)^2, where O is less then or equal to x which is less than or equal to 85 gix)=0.01 (x)^2+0.05x where O 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 (15) - 0.02(15 - 100)^2 $ 144.5 (per unit of drawing kit). charge per unit ss furvtion-$8.75. dde 144.5 3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of busines, she decides to supply 60 kits. How mach 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. gx) = 0.01x^2+0.06x X "quantity sold by Yasin in second month x-60 units g(60) = 0.01(60 2)+0.05(60) 0.01(3600)+0.05(60) 36+3 = $39 per kit when x-60 4. If Yaseen erentes 60 kits in her second month of business and offers them for sale at S66 ench, do you think she will sell all of them? Why or why not? No she will not sell all of them because 66-0.02 (x-100)2 x + sqaureroot 66/0.02 + 100 x-42.55 she can sell 43 kits. 5. What family of functions do fix) and g(x) belong to? How do you know? Both the functions f(x) and g(x) are part of the quadriatic family as they both have a degree of 2 6. If you were to graph two quadratie functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking 7. Use algebrnie methods to find where Yaseen's demand and supply functions intersect. What does this point(s) represent in context of this problem? Show all your work.