Pretend you are the "Sole" Producer of sandels for the Caribbean market. You have a Facility Capable of producing 150,000 pairs of cork-soled sandals per year. There are 80,000 feet that need sandals twice a year. The cost to start up/shut down the plant is $2000, and storage cost is $3 per pair per year. Assume no backorders.

Given,

Annual production capacity, P = 150000

Yearly Demand, D = 80000 sets

Set up cost, S = 2000

Storage cost, H = 3

x = 1-(D/P) = 1-(80000/150000) = 0.4667

a. Optimal number of pairs to deliver, Q = \sqrt{} (2DS/(H*x)) = \sqrt{} (2*80000*2000/(3*0.4667)) = 15118.04

b.The factory would be start each time sandals are produced. Number of productions = D/Q = 80000/15118.04= 5.29 times each year

c. Total expense = Total set up cost + Total storage cost = (D/Q)*S+(Q/2)*H*x = 5.29*2000+(15118.04/2)*3*0.4667 = 21163.38

d. Maximum level of inventory = Q*x = 15118.04*0.4667 = 7055.589

E) Now assume your sandals wear out very fast and people must buy a new pair every three months. What is the new optimal production level?

F) If consumers need only one pair per year, what is Q*? Does total inventory cost go up or down, and by what percentage?