Question (Newsboy problem): The decision maker in a supermarket must decide how many boxes of
bananas to order. The bananas come in boxes of 100 lbs, 500 lbs, and 1,000 lbs, and the decision maker
has determined to order exactly one of the three types of boxes. Naturally, there is a quantity discount:
each pound of bananas in the regular box costs 20¢, in the big box the price is 15¢ per pound, & in the
huge box it is 12¢ per pound. Demand has been estimated to be either 50 lbs, 250 lbs, 700 lbs, or 900 lbs
with probabilities of 0.3, 0.4, 0.2, and 0.1, respectively.
Bananas sell for 40¢ per pound, and customer demand must be satisfied. In case the store does not have
sufficient supplies, they must purchase them from one of their competitors for 60¢ per pound. Leftover
bananas have a salvage value of 5¢ per pound. Which of the boxes should be ordered and what is the
expected profit? Show all relevant computations.
Solution:
Demand
Regular box
Big box
Huge box
Probabilities
50 lbs
2.50
32.5
52.5
0.3
250 lbs
10
37.5
17.5
0.4
700 lbs
100
85
175
0.2
Expected
payoff
900 lbs
140
45
245
0.1
Recommendation: order a huge box, which will result in an expected payoff of $50.84.
37.25
26.75
50.84