Please read the problems carefully and do what you are asked to do. You can use the back page as a scratch paper. Suppose the total cost of producing the quantity q goods is given by (a) (2 points). 1. 2q2 + 12q + 1000. (b) (4 points). What is the pro t as a function of q if each item is sold for and every produced item is sold? (c) (8 points). Find the formulas for the marginal cost and marginal pro t. Find the equation of the line tangent to the curve of the function y = ex x = 1. Find the derivative of the function f (x) = (x + 1)x, x > 0. Hint: use the fact that x + 1 = eln(x+1), hence (x + 1)x = (eln(x+1))x = ex ln(x+1). Cost and revenue functions are given in the following gure. (a)(6 points).
