Question

Daily demands for loaves of bread at a grocery store are specified by following probability distribution: the store buys a loaf for 55 cents and sell it for $1.20 each. any unsold loaves at the end of the day are disposed of at 25 cents each. assume that the stock level is restricted to one of the demand levels specified for Pn.

n	100	150	200	250	300
Pn	0.20	0.25	0.30	0.15	0.10

1) Develop the associated decision tree.

2) How many loaves should be stocked daily?

Answer 1

a.

The decision tree is shown below

The decision matrix is shown below

n	100	150	200	250	300
Pn	0.2	0.25	0.3	0.15	0.1	Payoff
100	65	65	65	65	65	65
150	50	97.5	97.5	97.5	97.5	88
200	35	82.5	130	130	130	99.125
250	20	67.5	115	162.5	162.5	96
300	5	52.5	100	147.5	195	85.75

b.

The best expected value (payoff) is at stock of 200. That should be stocked.