The purchasing manager for a firm is trying to determine what the inventory level  should be for a particular product one month before the demand is known. She has  developed the following table, which gives the distribution of demand after one month  and the probabilities:

 

The unit selling price is $10. The unsold inventory has to be sold on a secondary market,  and the unit selling price on this secondary market is $1.

The manager prepares the inventory by placing orders with the supplier and the cost for  each unit is $5; for example, if she decides the inventory level to be 50, then she places  an order of 50 units with the supplier. Assume the order she placed is instantly received. 

However, the actual amount she receives might not coincide exactly with the order she  placed (due to the random production yield rate of the supplier), and the deviation has a distribution specified in the following table:

 

She only pays the cost for the actual amount she receives. For example, if she places an order of 50 units, then there is a 0.1 probability that she only receives 49 and she pays 49×$5 in such case.

(a) Create appropriate tables of interval of random numbers for the demand distribution  and the deviation distribution. 

(b) Use the "Table of Random Numbers" in appendix to generate 3 demands. 

(c) Use Monte Carlo simulation to estimate the profits associated with order quantity of  50 and 60, respectively, by generating 3 profit numbers for each order quantity. You can  re-use the numbers developed. Based on the estimated profits, compare the two  order quantities. 

Demand 40 50 60 70 80 Probability 0.20 0.25 0.25 0.20 0.10