8. A course has four exams, weighted 10%, 15%, 25%, and 50%. The class average on each of the four exams is 75%, 91%, 84%, and 87%, respectively. What do the vectors = (0.75, 0.91, 0.84, 0.87) and w = (0.1, 0.15, 0.25, 0.5) represent in terms of the course. Calculate the dot product w. a. What does it represent in terms of the course? 9. A manufacturer sells two products, one at a price of $4000 per unit and the other at a price of $13000 a unit. A quantity q1 of the first product and q of the second product are sold at a total daily cost of $(4000 + 1000q1+ 1000q2) to the manufacturer. a. Express the manufacturer's profit, P, as a function of q and q. Denote that function using proper notation. b. Carefully and accurately sketch contours of P for P = 10000, P = 20000, P = 30000, and the break-even curve P = 0. Your graph must have a labelled and scaled axis with clear and precise graphs on it. Interpret precisely what each contour curve represents.