Please show how to curate an example for this.

Math 31 Final Project 1. In this problem, you will design your own company selling whatever product you chose. What is your company and what is the product? What are the units (i.e. individual items or in packages)? Design your own supply curve of the form q = up + b by choosing two points of the form (19, q) corresponding to two prices and two quantities supplied at those prices. Design your own demand curve of the form q = cp + d by choosing two points of the form 0), q) corresponding to two prices and two quantities sold at those prices. . Graph the supply and demand curves and find the equilibrium price and quantity. Find the Consumers' Surplus and the Producers' Surplus at this equilibrium price and explain what these quantities mean. Draw the graph corresponding to your Consumers' Surplus and the graph corresponding to your Producers' Surplus. 2. In this problem, you will design your own continuous income stream R(t) for your company (this company does not have to be the same as your company in Problem #1). a. b. e. What is your company and what is the product? What is R(t)? Evaluate R(t) at several time points and explain why this choice makes sense. Find the total value for the income stream after some period of time. Imagine you are investing your continuous income stream at a continuously compounding interest rate of your choice. Find the future value at your time endpoint from part (c.). Find the present value corresponding to part (d.). 3. In this problem, you will design your own perpetuity as an endowment to SCU. Design a continuous income stream R(t) to be given to SCU for some period of time and evaluate at several time points. Determine how much you would need to deposit in an account paying some amount of continuously com pounded interest to allow this income stream to continue for 100 years. Determine how much you would need to deposit in an account paying some amount of continuously com pounded interest to allow this income stream to continue forever. 4. In this problem, you will make up your own Gini index for the distribution of wealth in a pretend country. Let's say your Lorentz curve is of the form f(x) = 3:\". Find the value of p that fits your made-up Gini index. b. Determine how much wealth is owned by each quartile of the population (i.e. 0% to 25%, 25% to 50%, 50% to 75% and 75% to 100%) using your value of p from part (a.) c. Add 1 to your value of p from part (a.) and recalculate your lGini index. Does your Gini index go up or down? Explain why this makes sense