1. The monthly forecast of demand for a product is provided below (i.e., a density and distribution function):

	F(x)	F(x)
0	0.0498	0.0498
1	0.1494	0.1991
2	0.2240	0.4232
3	0.2240	0.6472
4	0.1680	0.8153
5	0.1008	0.9161
6	0.0504	0.9665
7	0.0216	0.9881
8	0.0081	0.9962
9	0.0027	0.9989
10	0.0008	0.9997
11	0.0002	0.9999
12	0.0001	1.0000
13	0.0000	1.0000

 
If a company purchases a product in advance and doesn't actually need it, then the company will store it until it can be sold. The expected extra storage cost is $1250 per product. For example, if their needs are for 2 products but they advanced purchased 3, then they incur a $1250 charge for the 1 container that requires storage.

Product purchased on the spot market (after they learn their needs) are expected to cost $3500 per product. For example, the company may advance purchase 1 product but discover that they need 3, in which case the company would purchase an additional 2 products at $3500 each.

How many products should the company advance purchase to minimize their costs? (report your answer as an integer)

 

QUESTION 7

1. Weekly demand for a product is normally distributed with a mean of 50 and a standard deviation of 23. Demands are independent across weeks.

Orders are placed weekly and the lead time to receive an order is 2 weeks. The company wants to hold enough product to ensure a 98% in-stock probability. If they use an order up-to model, what base stock level should they implement? (report your answer as an integer)