1. Johnson wants to start a machine shop, but don’t know what size of shop he should invest in. This is his estimate of profit for good, average and bad market conditions

Profit Good Market Bad Market Average Market
Small Shop 10000 -20000 1000
Medium Shop 20000 -30000 5000
Large Shop 30000 -50000 8000
Probability 0.3 0.2 0.5

a. Please draw a decision tree illustrating the above situation.
b. What do you recommend based on maximax decision
c. What do you recommend based on EMV criterion
d. How would the recommendation change, based on EMV criterion, if the probability for a bad market is significantly higher than other types of market? (Hint: please use 0.8 or above for bad market)
2. Company X has the follows sales for the first 4 years.
Year Sales
1 130
2 140
3 156
4 164
5 ?

a. Use exponential smoothing with a weight of ? = 0.3, develop forecasts for years 2 through 5, assuming that the prediction for year 1 sales was 128
b. Use trend projection method, develop a forecasting model for the sales.
c. Which method is better? Please explain why and substantiate with numbers.
3. Beeliner Corporation makes washer/dryer combo units that use less energy. Orders have been received from vendors for the following months
MONTH UNITS
_____________________
Feb 170
Mar 230
April 230

Due to limited capacity, only 200 of these can be made on regular time, and the cost is $250. However, an extra 60 units per month can be produced on overtime. The cost is $285 instead. Also if there are any units produced that are not sold in that month, there is a cost of $10 to carry the item to the next month. Using linear programming, please help find the optimal solution for units to be produced during regular time and overtime (hints: you need 6 variables). What is the total cost of production to meet the orders for the three months?

4. To complete a rocket assembly at NASA, the engineers laid out the following tasks and came up with the time estimates for each activity below

Activity Immediate Predecessors A M b Crash cost per week
A – 1 3 5 $600
B – 2 4 6 $400
C – 4 5 6 $800
D A,B 2 3 4 $800
E A 4 6 8 $800
F C,D 1 2 3 $500
G E,F 1 2 3 $600
H G 1 2 3 $200

Please calculate the expected time and variance for each activity.
Which of the above activities are on the critical path?
If you need to crash the schedule, which of the activities above would you be willing to spend the crash cost?