3. Let s, and da denote the supply and demand at year n of the market, respectively, for certain product. We assume that dat1 = dn + (dn - Sn) + B(S. - Sat1), where a = -, 8 = :. We also assume the revenue of the company at year n is given by In = Sn(ydn - 6), where y = 2, 6 = 1. In the following set so = do = 10. (a) Given fixed d, and s,; show that [1] S(x) = r(Y(dn + (dn - Sn) + B(S. - I)) - 6) has a unique global maximum. This point is the level of supply say at year n + 1. We call this the greedy approach. (b) Find a matrix A and a vector b such that = A Sn + b . [2] (c) Find a vector u that u = Au + b. Show that Sn+1 - u = Anti dni+1 ((20) - 2.) . [4] (d) Write A' and A as scalars times A . Guess a general formula for A" for all n > 1 and [3] prove that your formula is correct. Find expressions for s,, and da- (c) Using the formula Ex - 1-att 1 x to write an exact explicit expression for the total [3] revenue of the company over the first ten years Reread = _-1