Question #1 (5 points) Management wants to design an assembly line that will turn out 800 videotapes per day. There will be eight working hours in each day. The industrial engineering staff has assembled the information below:

Task	Time (min.)	Immediate Follower
a	.2	b,d
b	.2	f
c	.4	b,e
d	.1	e
e	.3	f
f	.2	h
g	.1	h
h	.2	i
i	.6	none

1. Determine the optimum cycle time (i.e., actual operating time/desired output).
2. What is the minimum number of stations needed?
3. Assign tasks to work stations.
4. What is the efficiency of this assembly line?

Question #2 (5 points) Four samples of three observations each have been taken, with actual measurements (in centimeters) shown below. Construct x bar and R charts, and determine if the production process is under control.

Samples
1	2	3	4
12.3	11.9	12.0	12.1
12.2	12.2	12.2	11.8
12.1	12.2	11.8	11.8

Question #3 (5 points) Consider the following transportation decision-making information:

Plant	Capacity	Store	Demand
A	400	X	200
B	500	Y	250
C	100	Z	300
Total	1000	Total	750

Cost to ship from plant to store (per unit of demand)

Plant	Store
X	Y	Z
A	$2	$2	$3.5
B	$4	$5	$4.5
C	$3	$3	$3

1. Develop the following shipping assignment table that uses the Solver function to find the optimal shipping patterns between the plants and the stores.

Plant	Store
X	Y	Z
A
B
C

1. What is the minimal shipping cost?

Question #4 (5 points) The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior?

Quantity	Price
1 - 9	$2.95 per unit
10 - 999	$2.50 per unit
1,000 - 4,999	$2.30 per unit
5,000 or more	$1.85 per unit