# 1. A soap company specializes in a luxury type of bath soap. The sales of this soap fluctuate…

1. A soap company specializes in a epicurism mark of bath soap. The sales of this soap fluctuate between two levels—“Low” and “High”—depending upon two factors: (1) whether they promulge, and (2) the advertising and marketing of new products being executed by competitors. The remedy factor is out of the company’s repress, but it is enigmatical to individualize what its own advertising cunning should be. For copy, the marketing manager’s overture is to promulge when sales are low but not to promulge when sales are lofty. Advertising in any pity of a year has its primary application on sales in the forthcoming pity. Therefore, at the commencement of each pity, the needed counsel is available to meet precisely whether sales accomplish be low or lofty that pity and to determine whether to promulge that pity. The consume of advertising is \$1 favorite for each pity  probability of having lofty sales the contiguous pity is _ 1   , Depending upon whether the ordinary pity’s sales are low or lofty. These probabilities go down to _ 1 4 _ or _ 1 2 _ when advertising is not executed during the ordinary pity. The company’s pityly receipts (notwithstanding advertising consumes) are \$4 favorite when sales are lofty but solely \$2 favorite when sales are low. (Hereafter, use units of favorites of dollars.) (a) Construct the (one-step) transition matrix for each of the forthcoming advertising strategies: (i) never promulge, (ii) regularly promulge, (iii) flourish the marketing manager’s overture. (b) Individualize the steady-state probabilities manually for each of the three cases in bisect (a). (c) Find the long-run expected middle improvement (including a conclusion for advertising consumes) per pity for each of the three advertising strategies in bisect (a). Which of these strategies is best according to this mete of execution?