Quadratic Functions(in image)#7 - Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What does this point(s) represent in the context of this problem? Show all your work. When a company offers a new product or service, they estimate how much of that product orservice 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 theprice down.Companies use the estimated demand to determine how much of a product or service they arewilling to supply at different prices. As the price of a product or service incereases, companies arewilling 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 sometimesintersect 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 theamount of money she carns every month byselling at-home painting kits. These kits willinclude a photograph of the finished painting, alink and password to Yaseen's YouTube channelwhere she will provide detailed instructions anda step-by-step demonstration of how to createthe painting. The kit also contains the canvas,and all the paints the buyer will nced. Yaseenwill create a new kit for sale ench month.Yaseen estimates that the monthly demand for her painting kits can be modeled by the functionf(x) = 0.02(x - 100), where 0SIS 85. The number of kits that Yaseen can supply eachmonth is modeled by the function g(x) = 0.01x + 0.5x, where 0SIS 100. The value of xrepresents 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-linearequations to explore the questions below.1. Interpret the domain restrictions on the demand and the supply functions. What do theyrepresent in cotext of the scenario?demand function of price decrease from 200 to 4.5 demand 0 to 85Supply function g(100)-0.01x100 2=150SUpplv price increases as x quantitv (paint increases)2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she chargefor cach of these kits based on her supply function? How much should she charge for each ofthese kits based on her demand function? Show your work.f(x)=0.02 (x-100)^2. where O is less then or equal to x which is less than or equal to 85g(x)=0.01 (x)^2+0.05x where O is less than or equal to x which is less then or equal to100 , will be selling product at g(15)-0.01 (15)^2+0.05 x15 f(15) = 0.02(15 - 100)^2-S 144.5 (per unit of drawing kit). charge per unit ss funvtion=$9.75. dd= 144.53. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month ofbusiness, she decides to supply 60 kits. How much should she charge for cach of these kits basedon her supply function? How much should she charge for each of these kits based on her demandfunction? Show your work.g(x) = 0.01x^2+0.05xx =quantity sold by Yasin in second month x=60 unitsg(60) = 0.01(60°2)+0.05(60) = 0.01(3600)+0.05(60) = 36+3 = $39 per kit when x=604. If Yaseen creates 60 kits in her second month of business and offers them for sale at S66 each,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 . sgaureroot 66/0.02 +100 x=42.55 she can sell 43 kits.5. What family of functions do fix) and gix) belong to? How do you know?Both the functions f(x) and g(x) are part of the quadriatic family as they both have adegree of 2.6. If you were to graph two quadratic functions on the same xy-plane, how many intersectionpoints could there be? Use examples to explain your thinking7. Use algebraic methods to find where Yaseen's demand and supply functions intersect. Whatdoes this point(s) represent in context of this problem? Show all your work.

Question

Accepted Answer

7) Given that the monthly demand for her painting kits is given by fx=0.02x-1002,0≤x≤85.Also the…