A handbag company specializes in a luxury-type handbag. The sales of this handbag fluctuate between two levels- low and high- depending upon two factors: (1) whether they advertise and (2) the advertising and marketing of new products being done by competitors. The second factor is out of the company's control, but it is trying to determine what its own advertising policy should be. For example, the marketing manager's proposal is to advertise when sales are low, but not to advertise when sales are high. Advertising in any quarter of a year has its primary impact on sales in the following quarter. Therefore, at the beginning of each quarter, the needed information is available to forecast accurately whether sales will be low or high that quarter and to decide whether to advertise that quarter. The cost of advertising is $1 million for each quarter of a year in which it is done. When advertising is done during a quarter, the probability of having high sales the next quarter is 1/2 or 3/4, depending on whether the current quarter's sales are low or high. These probabilities go down to 1/4 or 1/2 when advertising is not done during the current quarter. The company's quarterly profits (excluding advertising costs) are $4 million when sales are high but only $2 million when sales are low. (Hereafter, use units of millions of dollars.) Part A: Construct a one-step transition matrix for each of the following advertising strategies: (i) never advertise, (ii) always advertise, and (iii) follow the marketing manager's proposal. (Attach answer and work.) Part B: Determine the steady-state probabilities for each of the three cases in part A. (Attach answer and work.) Part C: Find the long-run expected average profit (including a deduction for advertising costs) per quarter for each of the three advertising strategies in part A. (Attach answer and work.) Part D: Which of these strategies is best according to this measure of performance? (Use response box to enter answer.)