A firm manufactures dining room tables. The lead time for the table legs is uncertain. It can be 3 weeks with probability 0.15, 4 weeks with probability 0.4, 5 weeks with probability 0.25, or 6 weeks with probability 0.2. The inventory holding cost is $2 per unit per period (where a unit is a set of 4 legs). The underage cost is $9 per unit per period.

1. What is the best lead time for planning and the associated safety lead time?

2. Process improvement is proposed. How much would the underage cost need to be decreased to decrease the planning lead time by 1 week. (Hint: It may be easier to experiment with different underage costs to see which value results in the reduction using a spreadsheet rather than directly solve for the cost. Describe briefly what you did and verify the result.