118 the behavior of series of components plays a huge role in scientific and engineering reliability problems. the reliability of the entire system is certainly no better than that of the weakest component in the series. in a series system, the components operate independently of each other. in a particular system containing three components, the probabilities of meeting specifications for components 1, 2, and 3, respectively, are 0.95, 0.99, and 0.92. what is the probability that the entire system works

The board of directors is the highest ranking body in a corporation, and the chairman of the board is the highest ranking individual. the ceo generally works under the board and its chairman, and the board generally has the authority to remove the ceo under certain conditions. the ceo, however, cannot remove the board, but he or she can endeavor to have the board voted out and a new board voted in should a conflict arise. it is possible for a person to simultaneously serve as ceo and chairman of the board, though many corporate control experts believe it is bad to vest both offices in the same person. true false

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

M. cotteleer electronics supplies microcomputer circuitry to a company that incorporates microprocessors into refrigerators and other home appliances. one of the components has an annual demand of 235 units, and this is constant throughout the year. carrying cost is estimated to be $1.25 per unit per year, and the ordering (setup) cost is $21 per order. a) to minimize cost, how many units should be ordered each time an order is placed? b) how many orders per year are needed with the optimal policy? c) what is the average inventory if costs are minimized? d) suppose that the ordering cost is not $21, and cotteleer has been ordering 125 units each time an order is placed. for this order policy (of q = 125) to be optimal, determine what the ordering cost would have to be.