Question 1: A firm owns two manufacturing facilities that mamufacture the same item .The functions of the income are : P1= 8.5+ 0.03(x^2) and P2= 5.2+0.04(y^2) where x and y are the quantities produced by each facility .The relation between the selling price p and the total quantity q=x+y is p=60-0.04q What is the quantity that each facility should produce to maximize the firm's profits?
Question 2: Let f(x,y)= ln(x^2-y^2) and P(1;-1) Calculate the derivative at the following the direction vector u=(4;-3) at point P