Please answer all questions and provide clear formatting solution. Please provide detailed step by step solution for each question. The solution can be handwritten or pdf. Thanks

Calculus 1. Suppose the supply and demand curves for a particular commodity are S(q) = \\/q? + 200g and D(qg) = 100 g. (a) Find the equilibrium quantity g* and price p*. (b) Find the consumer surplus. 2. Suppose the income from advertisements on a blog for the next 2 years is given by the income stream f(t) = 200t + 100e~**, where t is the year (t = 0 being now) and f(t) is the rate of income in dollars per year. The interest rate is set at 10% p.a. (a) Calculate the total income over the next 2 years. Give your final answer rounded to the nearest cent. (b) Calculate the present value of the income stream. It should in- volve integration by parts. Give your final answer rounded to the nearest cent. Two Variable Calculus 3. Let f(x,y) = (x? + 4y)e. (a) Find the critical point(s). (b) Use the second derivative test to classify the critical point(s)