Chapter 5.4, Problem 28E

PortaCom has developed a design for a high-quality portable printer. The two key components of manufacturing cost are direct labor and parts. During a testing period, the company has developed prototypes and conducted extensive product tests with the new printer. PortaCom’s engineers have developed the bivariate probability distribution shown below for the manufacturing costs. Parts cost (in dollars) per printer is represented by the random variable x and direct labor cost (in dollars) per printer is represented by the random variable y. Management would like to use this probability distribution to estimate manufacturing costs.

Parts (x)	Direct Labor (y)    43      45    48			Total
85	0.05	0.2	0.2	0.45
95	0.25	0.2	0.1	0.55
Total	0.30	0.4	0.3	1.00

1. a. Show the marginal distribution of direct labor cost and compute its expected value, variance, and standard deviation.
2. b. Show the marginal distribution of parts cost and compute its expected value, variance, and standard deviation.
3. c. Total manufacturing cost per unit is the sum of direct labor cost and parts cost. Show the probability distribution for total manufacturing cost per unit.
4. d. Compute the expected value, variance, and standard deviation of total manufacturing cost per unit.
5. e. Are direct labor and parts costs independent? Why or why not? If you conclude that they are not, what is the relationship between direct labor and parts cost?
6. f. PortaCom produced 1500 printers for its product introduction. The total manufacturing cost was $198,350. Is that about what you would expect? If it is higher or lower, what do you think may have caused it?