Weekly demand for a particular item averages 30 units, with a standard deviation of 4. This item is managed with a fixed-order-interval model. The order interval is three weeks, and this item has a certain lead time of one week. The desired service level is 97.5 percent. Assume that it is now time to place another order, and there are 43 units on hand. How many units should be ordered?
A. 63
B. 93
B. 83
D. None of the above

(B)93

Explanation:

Since we are using a fixed-order-interval model,

The Amount to Order=Expected Demand During protection Interval+Safety Stock-Amount at Hand

Where:  

d=weekly demand

OI=Order Interval

LT=Lead Time

z=Standard Deviation of Desired Service Level

=Standard Deviation of weekly Demand

A= Amount at Hand

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional