Economic mathematics

  Suppose a firm sells a good q and the production function of good q is 16q = 65 - 2(x - 5)2 - 4(y - 4)2 the price unit of the good q is 32 and the unit prices of inputs x and y are 8 and 4 , respectively. 4.1. Derive the total revenue function of this firm (2 points) 4.2. Derive the profit function of this firm ( 2 points) 4.3. Find quantity of inputs x and y that maximize profit 4.4. Test the second order conditions of the profit maximization What is the maximum profit? What is the output level, q, at the maximum profit?