5. For the function, f (x) = -a2 + 2x - 3, find the vertex and determine whether this vertex is a maximum or minimum. (2 marks) 6. The cost and revenue functions for making and selling q picture frames are given respectively by C (q) = 15q + 40 and R(q) = 20q - 0.1q2 . (8 marks) a. Find and simplify the profit function and give its domain. b. Find the break-even quantity. c. Find the quantity q that maximizes the profit. d. What is the maximum profit? 7. The price function for a manufacturer's product is p = 80 - 2q, where p is in dollars per unit and q is the number of units are produced. Find the level of production that maximizes the manufacturer's total revenue and determine this revenue. (3 marks) 8. The supply and demand functions for q boxes of napkins at a price p per box are: Supply: p - Vq =6 Demand: q + p = 12. Find the equilibrium price and quantity