#4 handwritten 1. Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. Onthis wall, Raul paints two waves to the shape of the following functions:f: y = (x + ¹)(x + 1)(x - 1)(2x)y = (2x +2)(2x – 2)(x)(−x −}}He plans to paint the region between the two waves a dark black.(a) Graph/draw Raul's artwork. Label the functions and all intersection points.(Note: You may use a graphing software to help you with the graph, but do not just take a screenshot.)(b) If dark black paint costs P10 per sq. unit, how much would it cost to finish the artwork?2. The Lorenz curve of a particular society is given byL(x) = Ax² + Bx.Suppose that the poorest half of the population receive only 35% of the society's income andthat the Gini index of this society is 0.2. Find A and B.3. The price-supply and price-demand equations of a certain product are given byp= S(x)=15+0.1x+0.003x², p=D(x) = M - NxSuppose that the equilibrium price level is P55.(a) Find the producer surplus at the equilibrium price level.(b) If the consumer surplus is equal to the producers surplus at the equilibrium price level,find M and N.4. A decorator, who is a monopolist, makes two types of specialty picture frames. From experience,the decorator has determined that if x frames of the first type and y frames of the second typeare made and put on sale in a showroom, they can be sold for (100-2x) dollars and (120-3y)dollars each, respectively.The total cost of constructing these frames is (12x+12y + 4xy) dollars. How many frames ofeach type should be produced to realize the maximum profit, and what is the maximum profit?Make sure to verify that this is indeed a maximum.

4. A decorator, who is a monopolist, makes two types of specialty picture frames. From experience, the decorator has determined that if x frames of the first type and y frames of the second type are made and put on sale in a showroom, they can be sold for (100 – 2x) dallars and (120 – 3y) dollars each, respectively. The total cost of constructing these frames is (12x +12y +4xy) dollars. How many frames of each type should be produced to realize the maximum profit, and what is the maximum profit? Make sure to verify that this is indeed a maximum.