High Plains Inc. manufacturers furniture in North Dakota. High Plains receives its

a. On average, the number of boards they have on order  = 1,056 boards.

b. On average, the number of boards they have =560 boards.

c. Total holding cost per week = $140.

d. Holding cost incurred per board = $ 0.25.

Explanation:

In the question, the details given are:

Service level =96 %

Lead time =3 weeks

Weekly demand =150

Standard deviation=200

This is a case of variable demand and constant lead time

a. Reorder point =Demand during lead time +Safety stock

=Average weekly demand*lead time+z*sqrt(lead time)*standard deviation of weekly demand

=150*3+NORMSINV(0.99)*sqrt(3)*200

=450+1.7507*sqrt(3)*200

=450+606.46=1,056.46

=1,056 (nearest whole number).

On average, the number of boards they have on order  = 1,056 boards.

b. For a normal distribution,

z=x-mean/std deviation

z-value for a 96% confidence level = 2.05

2.05=x-150/200

x = 150+2.05*200=560

On average, the number of boards they have =560 boards.

c.Total holding cost per week=Average inventory *holding cost per week=560/2 *0.5=280*0.5 =$140

d.Holding cost incurred per board =Total holding cost /Number of boards =140/560 = $ 0.25.