Please answer all questions and provide step-by-step solution for each question.

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)