3. The AE brick company has been operating two plants A and E in a region. The market for bricks is competitive, although there are only four regional suppliers: AE and three other firms B,C,D, who operate one plant each. An operating plant incurs principally labor and material costs, and can produce output up to the designed capacity limit for that plant. The market demand curve for bricks is given by p = 5.75 - 9/100 where q is in thousands. An analyst has provided the following estimates of costs and capacities of the five plants. Plant Cost Capacity (dollars/brick) (thousands) 1.80 100 A B 2.00 50 2.60 50 D 2.70 50 E 3.00 75 (a) Determine a simple algebraic equation for the cost function for AE. Your equation may have two parts. (b) Sketch (fairly accurately) the industry supply curve. (c) What is the equilibrium price of bricka? (d) For each firm, calculate the equilibrium production levels, and producer surplus