6. (i) (10 pts) Consider an economy with two good X and Y with prices px and py respectively. Suppose an agent has an income w. Show that B := {(x, y) E R2 : pxx + Pyy = w} is a closed set in (R2, d2). (ii) (10 pts) Consider a market with a linear demand function p = a - Bq and a single firm. The firm faces a a cost function given by c(q) = cq2. Write down the profit function of the firm x(q). Is this function continuous for all qER