Problem $1($EOQ$)[50$ pts$]$

You are in charge of the replenishment of a critical component A which is purchased from an outside supplier.

You have estimated that the annual demand for component A is $20,000$ units. The purchasing cost of one

component of A is $$50$ dollars. Placing an order to the outside supplier has a fixed cost of $$500$ and a fixed lead$-$

time of $2$ weeks. The cost of capital is $20\%($take this one as the holding cost$)$ of the purchasing cost. Assume $52$

weeks in a year.

a$)$ Using the EOQ model, determine the optimal ordering level for component A$.[14$ points$]$

b$)$ What is the inventory turnover for component A per year? $[12$ points$]$

c$)$ What are the annual holding, fixed ordering, purchasing and total costs associated to component A$?[12$

points$]$

d$)$ What is the optimal Reorder Point for component A$?[12$ points$]$

Problem $2($Newsvendor Model$)[50$ pts$]$

Tom owns a small firm that manufactures "Tom Sunglasses". He has the opportunity to sell a particular seasonal

model to Land's End. Tom offers Land's End two purchasing options:

Option $1.$ Tom offers a price of $$46$ for each unit, but returns are no longer accepted. In this case, Land's

End throws out unsold units at the end of the season.

Option $2.$ Tom offers to set his price at $$60$ and agrees to credit Land's End $$52$ for each unit Land's

End returns to Tom at the end of the season.

This season's demand for this model will be normally distributed with mean of $210$ and standard deviation of

Land's End will sell those sunglasses for $$110$ each.

a$)$ How much would Land's End buy if they choose option $1?[25$ points$]$

b$)$ How much would Land's End buy if they choose option $2?$ What is the probability that Land's End will

return sunglasses to Tom at the end of the season? $[25$ points$]$