Due: Friday, Feb. 13, 1998, 5:00pm, in the dropbox, Rosebrugh Building, 2nd Floor.

Question #1: A production engineer is faced with decision to purchase a new machine to be used in manufacturing a new product. It is not known surely in advance how long the need for the product will continue in the market, but it is generally believed that it will not last more than 8 yr. Four types of machines are available, M1, M2, M3, and M4, with expected lives of 2,4,6, and 8 yr., respectively. Cost and return data have been estimated for each of the four machines, assuming four different market conditions, S1, S2, S3, and S4, corresponding to 2,4,6, and 8 yr. of product survival in the market. An expert of the market assigns certain probabilities to each of the market conditions. These probabilities are 0.2, 0.3, 0.4, and 0.1, corresponding to S1, S2, S3, and S4, respectively. The following matrix shows the present worth of the net return of each machine under each possible market conditions. (Numbers in the matrix corresponds to $1,000)

	S1 (0.2)	S2 (0.3)	S3 (0.4)	S4 (0.1)
M1	100	90	80	70
M2	60	110	110	90
M3	-50	90	150	140
M4	-30	80	100	200

(a) Suppose that the management sets a minimum aspiration level for profit of $120,000, and maximum aspiration level for loss of $40,000. State the best alternative(s) selected by using the aspiration level criterion. (1 pt.)

(b) State the best alternative by using the most probable future criterion. (1 pt.)

(c) State the best alternative by using expected value criterion. (1 pt.)

(d) Suppose that the probabilities are not available. So state the best alternative by using the Laplace criterion. (1 pt.)

(e) Suppose that the probabilities are not available. So state the best alternatives by using the Maximin and Maximax criteria. (2pts.)

(f) Suppose that the probabilities are not available. So state the best alternative by using the Hurwicz criterion (the alpha value for the Hurwicz criterion is 0.4) . (1.5 pts.)